Factor Difference of Two Squares (Harder) 1

Question 1 of 5

Factor.

2 y^{2} - 18

$2y^2-18$

1. $2 (y - 3) (y + 3)$ $2(y-3)(y+3)$
2. $(y - 3) (y + 3)$ $(y-3)(y+3)$
3. $2 (y^{2} - 3)$ $2(y^2-3)$
4. $2 (y - 3) (y^{2})$ $2(y-3)(y^2)$

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

Factoring the Difference of Two Squares

a^{2} - b^{2} = (a - b) (a + b)

$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2=(\color{#00880A}{a}-\color{#9a00c7}{b})(\color{#00880A}{a}+\color{#9a00c7}{b})$

First, find the Greatest Common Factor (GCF) of the two terms.

Start by listing down their factors.

Factors of

2 y^{2}

$2y^2$ : $2$ $2$

\times y \times y

$timesytimesy$

Factors of

18

$18$ : $2$ $2$

\times 9

$times9$

Both

2 y^{2}

$2y^2$ and

18

$18$ have

2

$2$ as their factor, so it is the GCF.

Next, factor by placing

2

$2$ outside a bracket.

Also, place the given polynomial inside the bracket with each term divided by

2

$2$ , then simplify.

		$2 [(2 y^{2} \div 2) - (18 \div 2)]$ $2[(2y^2div2)-(18div2)]$
	$=$ $=$	$2 (y^{2} - 9)$ $2(y^2-9)$

Now, express both terms inside the parenthesis as perfect squares. In other words, both terms should have

2

$2$ as their exponent.

		$y^{2} - 9$ $y^2-9$
	$=$ $=$	$y^{2} - 3^{2}$ $y^2-3^2$	$3^{2} = 9$ $3^2=9$

Finally, label the values in the expression

2 y^{2} - 18

$2y^2-18$ and substitute the values into the formula given for Factoring the Difference of Two Squares.

a = y

$a=y$

b = 3

$b=3$

$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$	$=$ $=$	$(\color{#00880A}{a}-\color{#9a00c7}{b})(\color{#00880A}{a}+\color{#9a00c7}{b})$
$2(\color{#00880A}{y}^2-\color{#9a00c7}{3}^2)$	$=$ $=$	$2(\color{#00880A}{y}-\color{#9a00c7}{3})(\color{#00880A}{y}+\color{#9a00c7}{3})$

2 (y - 3) (y + 3)

$2(y-3)(y+3)$

Question 2 of 5

Factor.

5 x^{2} - 500

$5x^2-500$

1. $5 (x - 10) (x + 50)$ $5(x-10)(x+50)$
2. $5 (x - 10) (x + 10)$ $5(x-10)(x+10)$
3. $10 (x - 5) (x + 5)$ $10(x-5)(x+5)$
4. $10 (x - 10) (x + 5)$ $10(x-10)(x+5)$

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

Factoring the Difference of Two Squares

a^{2} - b^{2} = (a - b) (a + b)

$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2=(\color{#00880A}{a}-\color{#9a00c7}{b})(\color{#00880A}{a}+\color{#9a00c7}{b})$

First, find the Greatest Common Factor (GCF) of the two terms.

Start by listing down their factors.

Factors of

5 x^{2}

$5x^2$ : $5$ $5$

\times x \times x

$timesxtimesx$

Factors of

500

$500$ : $5$ $5$

\times 100

$times100$

Both

5 x^{2}

$5x^2$ and

500

$500$ have

5

$5$ as their factor, so it is the GCF.

Next, factor by placing

5

$5$ outside a bracket.

Also, place the given polynomial inside the bracket with each term divided by

5

$5$ , then simplify.

		$5 [(5 x^{2} \div 5) - (500 \div 5)]$ $5[(5x^2div5)-(500div5)]$
	$=$ $=$	$5 (x^{2} - 100)$ $5(x^2-100)$

Now, express both terms inside the parenthesis as perfect squares. In other words, both terms should have

2

$2$ as their exponent.

		$x^{2} - 100$ $x^2-100$
	$=$ $=$	$x^{2} - 10^{2}$ $x^2-10^2$	$10^{2} = 100$ $10^2=100$

Finally, label the values in the expression

5 x^{2} - 500

$5x^2-500$ and substitute the values into the formula given for Factoring the Difference of Two Squares.

a = x

$a=x$

b = 10

$b=10$

$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$	$=$ $=$	$(\color{#00880A}{a}-\color{#9a00c7}{b})(\color{#00880A}{a}+\color{#9a00c7}{b})$
$5(\color{#00880A}{x}^2-\color{#9a00c7}{10}^2)$	$=$ $=$	$5(\color{#00880A}{x}-\color{#9a00c7}{10})(\color{#00880A}{x}+\color{#9a00c7}{10})$

5 (x - 10) (x + 10)

$5(x-10)(x+10)$

Question 3 of 5

Factor.

63 - 7 b^{2}

$63-7b^2$

1. $7 (3 - b) (3 + b)$ $7(3-b)(3+b)$
2. $9 (7 - b) (7 + b)$ $9(7-b)(7+b)$
3. $9 (3 - b) (7 + b)$ $9(3-b)(7+b)$
4. $7 (9 - b) (9 + b)$ $7(9-b)(9+b)$

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

Factoring the Difference of Two Squares

a^{2} - b^{2} = (a - b) (a + b)

$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2=(\color{#00880A}{a}-\color{#9a00c7}{b})(\color{#00880A}{a}+\color{#9a00c7}{b})$

First, find the Greatest Common Factor (GCF) of the two terms.

Start by listing down their factors.

Factors of

63

$63$ : $7$ $7$

\times 9

$times9$

Factors of

7 b^{2}

$7b^2$ : $7$ $7$

\times b \times b

$timesbtimesb$

Both

63

$63$ and

7 b^{2}

$7b^2$ have

7

$7$ as their factor, so it is the GCF.

Next, factor by placing

7

$7$ outside a bracket.

Also, place the given polynomial inside the bracket with each term divided by

7

$7$ , then simplify.

		$7 [(63 \div 7) - (7 b^{2} \div 7)]$ $7[(63div7)-(7b^2div7)]$
	$=$ $=$	$7 (9 - b^{2})$ $7(9-b^2)$

Now, express both terms inside the parenthesis as perfect squares. In other words, both terms should have

2

$2$ as their exponent.

		$9 - b^{2}$ $9-b^2$
	$=$ $=$	$3^{2} - b^{2}$ $3^2-b^2$	$3^{2} = 9$ $3^2=9$

Finally, label the values in the expression

63 - 7 b^{2}

$63-7b^2$ and substitute the values into the formula given for Factoring the Difference of Two Squares.

a = 3

$a=3$

b = b

$b=b$

$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$	$=$ $=$	$(\color{#00880A}{a}-\color{#9a00c7}{b})(\color{#00880A}{a}+\color{#9a00c7}{b})$
$7(\color{#00880A}{3}^2-\color{#9a00c7}{b}^2)$	$=$ $=$	$7(\color{#00880A}{3}-\color{#9a00c7}{b})(\color{#00880A}{3}+\color{#9a00c7}{b})$

7 (3 - b) (3 + b)

$7(3-b)(3+b)$

Question 4 of 5

Factor.

54 m^{3} - 24 m

$54m^3-24m$

1. $5 m (2 m - 3) (3 m + 2)$ $5m(2m-3)(3m+2)$
2. $8 m (6 m - 2) (3 m + 2)$ $8m(6m-2)(3m+2)$
3. $12 m (3 m - 2) (2 m + 2)$ $12m(3m-2)(2m+2)$
4. $6 m (3 m - 2) (3 m + 2)$ $6m(3m-2)(3m+2)$

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

Factoring the Difference of Two Squares

a^{2} - b^{2} = (a - b) (a + b)

$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2=(\color{#00880A}{a}-\color{#9a00c7}{b})(\color{#00880A}{a}+\color{#9a00c7}{b})$

First, find the Greatest Common Factor (GCF) of the two terms.

Start by listing down their factors.

Factors of

54 m^{3}

$54m^3$ : $6$ $6$

\times 9 \times

$times9times$ $m$ $m$

\times m \times m

$timesmtimesm$

Factors of

24 m

$24m$ :

4 \times

$4times$ $6$ $6$

\times

$times$ $m$ $m$

Collect the common factors and multiply them all to get the GCF.

GCF	$=$ $=$	$6$ $6$ $\times$ $times$ $m$ $m$
	$=$ $=$	$6 m$ $6m$

Next, factor by placing

6 m

$6m$ outside a bracket.

Also, place the given polynomial inside the bracket with each term divided by

6 m

$6m$ , then simplify.

		$6 m [(54 m^{3} \div 6 m) - (24 m \div 6 m)]$ $6m[(54m^3div6m)-(24mdiv6m)]$
	$=$ $=$	$6 m (9 m^{2} - 4)$ $6m(9m^2-4)$

Now, express both terms inside the parenthesis as perfect squares. In other words, both terms should have

2

$2$ as their exponent.

	$9 m^{2} - 4$ $9m^2-4$
$=$ $=$	${(3 m)}^{2} - 4$ $(3m)^2-4$	${(3 m)}^{2} = 9 m^{2}$ $(3m)^2=9m^2$
$=$ $=$	${(3 m)}^{2} - 2^{2}$ $(3m)^2-2^2$	$2^{2} = 4$ $2^2=4$

Finally, label the values in the expression

54 m^{3} - 24 m

$54m^3-24m$ and substitute the values into the formula given for Factoring the Difference of Two Squares.

a = 3 m

$a=3m$

b = 4

$b=4$

$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$	$=$ $=$	$(\color{#00880A}{a}-\color{#9a00c7}{b})(\color{#00880A}{a}+\color{#9a00c7}{b})$
$6m[(\color{#00880A}{3m})^2-\color{#9a00c7}{2}^2]$	$=$ $=$	$6m(\color{#00880A}{3m}-\color{#9a00c7}{2})(\color{#00880A}{3m}+\color{#9a00c7}{2})$

6 m (3 m - 2) (3 m + 2)

$6m(3m-2)(3m+2)$

Question 5 of 5

Factor.

72 x - 32 x^{3}

$72x-32x^3$

1. $8 x (3 - 2 x) (3 + 2 x)$ $8x(3-2x)(3+2x)$
2. $8 x (3 - x^{2}) (3 + 2 x)$ $8x(3-x^2)(3+2x)$
3. $8 x (3 - x^{2}) (3 + 4 x)$ $8x(3-x^2)(3+4x)$
4. $8 x (9 - 2 x) (4 + 2 x)$ $8x(9-2x)(4+2x)$

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

Factoring the Difference of Two Squares

a^{2} - b^{2} = (a - b) (a + b)

$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2=(\color{#00880A}{a}-\color{#9a00c7}{b})(\color{#00880A}{a}+\color{#9a00c7}{b})$

First, find the Greatest Common Factor (GCF) of the two terms.

Start by listing down their factors.

Factors of

72 x

$72x$ : $8$ $8$

\times 9 \times

$times9times$ $x$ $x$ `

Factors of

32 x^{3}

$32x^3$ :

4 \times

$4times$ $8$ $8$

\times

$times$ $x$ $x$

\times x \times x

$timesxtimesx$

Collect the common factors and multiply them all to get the GCF.

GCF	$=$ $=$	$8$ $8$ $\times$ $times$ $x$ $x$
	$=$ $=$	$8 x$ $8x$

Next, factor by placing

8 x

$8x$ outside a bracket.

Also, place the given polynomial inside the bracket with each term divided by

8 x

$8x$ , then simplify.

		$8 x [(72 x \div 8 x) - (32 x^{3} \div 8 x)]$ $8x[(72xdiv8x)-(32x^3div8x)]$
	$=$ $=$	$8 x (9 - 4 x^{2})$ $8x(9-4x^2)$

Now, express both terms inside the parenthesis as perfect squares. In other words, both terms should have

2

$2$ as their exponent.

	$9 - 4 x^{2}$ $9-4x^2$
$=$ $=$	$3^{2} - 4 x^{2}$ $3^2-4x^2$	$3^{2} = 9$ $3^2=9$
$=$ $=$	$3^{2} - {(2 x)}^{2}$ $3^2-(2x)^2$	${(2 x)}^{2} = 4 x^{2}$ $(2x)^2=4x^2$

Finally, label the values in the expression

72 x - 32 x^{3}

$72x-32x^3$ and substitute the values into the formula given for Factoring the Difference of Two Squares.

a = 3

$a=3$

b = 2 x

$b=2x$

$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$	$=$ $=$	$(\color{#00880A}{a}-\color{#9a00c7}{b})(\color{#00880A}{a}+\color{#9a00c7}{b})$
$8x[\color{#00880A}{3}^2-(\color{#9a00c7}{2x})^2]$	$=$ $=$	$8x(\color{#00880A}{3}-\color{#9a00c7}{2x})(\color{#00880A}{3}+\color{#9a00c7}{2x})$

8 x (3 - 2 x) (3 + 2 x)

$8x(3-2x)(3+2x)$

Factor Difference of Two Squares (Harder) 1

Try VividMath Premium to unlock full access

Quiz summary

Information

1. Question

Hint

Excellent!

Factoring the Difference of Two Squares

2. Question

Hint

Fantastic!

Factoring the Difference of Two Squares

3. Question

Hint

Nice Job!

Factoring the Difference of Two Squares

4. Question

Hint

Keep Going!

Factoring the Difference of Two Squares

5. Question

Hint

Well Done!

Factoring the Difference of Two Squares

Quizzes