Factor Quadratics (Complex)

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Question 1 of 5

Factorise.

21 + 43 a + 20 a^{2}

$21+43a+20a^2$

1. $(7 + 5 a) (3 + 4 a)$ $(7+5a)(3+4a)$
2. $(7 + 10 a) (3 + 2 a)$ $(7+10a)(3+2a)$
3. $(7 + 20 a) (3 + a)$ $(7+20a)(3+a)$
4. $(7 + 3 a) (3 + 6 a)$ $(7+3a)(3+6a)$

	Product	Sum when Cross-Multiplied
$2 a$ $2a$ and $10 a$ $10a$	$20 a^{2}$ $20a^2$	$(3 \times 2 a) + (7 \times 10 a) = 76 a$ $(3times2a)+(7times10a)=76a$
$5 a$ $5a$ and $4 a$ $4a$	$20 a^{2}$ $20a^2$	$(3 \times 5 a) + (7 \times 4 a) = 43 a$ $(3times5a)+(7times4a)=43a$
$20 a$ $20a$ and $1 a$ $1a$	$20 a^{2}$ $20a^2$	$(3 \times 20 a) + (7 \times 1 a) = 67 a$ $(3times20a)+(7times1a)=67a$

Question 2 of 5

Factorise.

56 + 19 y - 10 y^{2}

$56+19y-10y^2$

1. $(7 - 2 y) (8 + 5 y)$ $(7-2y)(8+5y)$
2. $(7 + 2 y) (8 - 5 y)$ $(7+2y)(8-5y)$
3. $(7 + y) (8 - 10 y)$ $(7+y)(8-10y)$
4. $(7 - y) (8 + 10 y)$ $(7-y)(8+10y)$

Question 3 of 5

3. Question
Factorise.

$x^2+5xy+4y^2$
- 1. $(x+2y)(x-2y)$
- 2. $(x-y)(x+4y)$
- 3. $(x+2y)(x+2y)$
- 4. $(x+4y)(x+y)$
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When factorising trinomials, use the Cross Method.

Use the cross method to factorise $x^2+5xy+4y^2$

Start by drawing a cross.

Now, find two values that will multiply into $x^2$ and write them on the left side of the cross.

$x$ and $x$ fits this description.

Next, find two numbers that will multiply into $4y^2$ and, when cross-multiplied to the values to the left side, will add up to $5xy$ .

Product Sum when Cross-Multiplied

$2y$ and $2y$ $4y^2$ $(xtimes2y)+(xtimes2y)=4xy$

$4y$ and $y$ $4y^2$ $(xtimes4y)+(xtimesy)=5xy$

$4y$ and $y$ fits this description.

Now, write $4y$ and $y$ on the right side of the cross.

Finally, group the values in a row with a bracket and combine the brackets.

Therefore, the factorised expression is $(x+4y)(x+y)$ .

$(x+4y)(x+y)$
Question 4 of 5

4. Question
Factorise.

$6x^2+xy-2y^2$
- 1. $(2x-y)(3x+2y)$
- 2. $(6x-y)(x+2y)$
- 3. $(2x-2y)(3x+y)$
- 4. $(6x-2y)(x+y)$
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When factorising trinomials, use the Cross Method.

Use the cross method to factorise $6x^2+xy-2y^2$

Start by drawing a cross.

Now, find two values that will multiply into $6x^2$ and write them on the left side of the cross.

Either $6x$ and $x$ or $2x$ and $3x$ fits this description. Try $2x$ and $3x$ first.

Next, find two numbers that will multiply into $-2y^2$ and, when cross-multiplied to the values to the left side, will add up to $xy$ .

Product Sum when Cross-Multiplied

$-2y$ and $y$ $-2y^2$ $(3xtimes-2y)+(2xtimesy)=-4xy$

$-y$ and $2y$ $-2y^2$ $(3xtimes-y)+(2xtimes2y)=xy$

$-y$ and $2y$ fits this description.

Now, write $-y$ and $2y$ on the right side of the cross.

Finally, group the values in a row with a bracket and combine the brackets.

Therefore, the factorised expression is $(2x-y)(3x+2y)$ .

$(2x-y)(3x+2y)$
Question 5 of 5

5. Question
Factorise.

$28x^2+xy-2y^2$
- 1. $(2x-y)(14x+2y)$
- 2. $(2x+2y)(14x-y)$
- 3. $(7x+2y)(4x-y)$
- 4. $(7x-y)(4x+2y)$
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When factorising trinomials, use the Cross Method.

Use the cross method to factorise $28x^2+xy-2y^2$

Start by drawing a cross.

Now, find two values that will multiply into $-2y^2$ and write them on the left side of the cross.

$-2y$ and $y$ fits this description.

Next, find two numbers that will multiply into $28x^2$ and, when cross-multiplied to the values to the left side, will add up to $xy$ .

Product Sum when Cross-Multiplied

$2x$ and $14x$ $28x^2$ $(2xtimesy)+(14xtimes-2y)=-26xy$

$7x$ and $4x$ $28x^2$ $(7xtimesy)+(4xtimes-2y)=xy$

$7x$ and $4x$ fits this description.

Now, write $7x$ and $4x$ on the right side of the cross.

Finally, group the values in a row with a bracket and combine the brackets.

Therefore, the factorised expression is $(7x+2y)(4x-y)$ .

$(7x+2y)(4x-y)$

	Product	Sum when Cross-Multiplied
$- y$ $-y$ and $10 y$ $10y$	$- 10 y^{2}$ $-10y^2$	$(8 \times - y) + (7 \times 10 y) = 62 y$ $(8times-y)+(7times10y)=62y$
$- 2 y$ $-2y$ and $5 y$ $5y$	$- 10 y^{2}$ $-10y^2$	$(8 \times - 2 y) + (7 \times 5 y) = 19 y$ $(8times-2y)+(7times5y)=19y$

Factor Quadratics (Complex)

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Quiz summary

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1. Question

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Quizzes

	Product	Sum when Cross-Multiplied
$2y$ and $2y$	$4y^2$	$(xtimes2y)+(xtimes2y)=4xy$
$4y$ and $y$	$4y^2$	$(xtimes4y)+(xtimesy)=5xy$

	Product	Sum when Cross-Multiplied
$-2y$ and $y$	$-2y^2$	$(3xtimes-2y)+(2xtimesy)=-4xy$
$-y$ and $2y$	$-2y^2$	$(3xtimes-y)+(2xtimes2y)=xy$

	Product	Sum when Cross-Multiplied
$2x$ and $14x$	$28x^2$	$(2xtimesy)+(14xtimes-2y)=-26xy$
$7x$ and $4x$	$28x^2$	$(7xtimesy)+(4xtimes-2y)=xy$