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Question 1 of 4
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First, find the Greatest Common Factor (GCF) of the two terms.
Start by listing down their factors.
Factors of 2x5: 2×x×x×x×x×x
Factors of 128x3: 2×64×x×x×x
Collect the common factors and multiply them all to get the GCF.
Next, factor by placing 2x3 outside a bracket.
Also, place the given polynomial inside the bracket with each term divided by 2x3, then simplify.
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2x3[(2x5÷2x3)-(128x3÷2x3)] |
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= |
2x3(x2-64) |
Now, express both terms inside the parenthesis as perfect squares. In other words, both terms should have 2 as their exponent.
Finally, label the values in the expression x2-82 and substitute the values into the formula given for Factoring the Difference of Two Squares.
a2−b2 |
= |
(a−b)(a+b) |
2x3(x2−82) |
= |
2x3(x−8)(x+8) |
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Question 2 of 4
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First, find the Greatest Common Factor (GCF) of the two terms.
Start by listing down their factors.
Factors of 3x2y2: 3×x×x×y×y
Factors of 3: 1×3
Both 3x2y2 and 3 have 3 as their factor, so it is the GCF.
Next, factor by placing 3 outside a bracket.
Also, place the given polynomial inside the bracket with each term divided by 3, then simplify.
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3[(3x2y2÷3)-(3÷3)] |
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= |
3(x2y2-1) |
Now, express both terms inside the parenthesis as perfect squares. In other words, both terms should have 2 as their exponent.
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x2y2-1 |
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= |
(xy)2-1 |
(xy)2=x2y2 |
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= |
(xy)2-12 |
12=1 |
Finally, label the values in the expression (xy)2-12 and substitute the values into the formula given for Factoring the Difference of Two Squares.
a2−b2 |
= |
(a−b)(a+b) |
3[(xy)2−12] |
= |
3(xy−1)(xy+1) |
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Question 3 of 4
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First, express both terms inside the parenthesis as perfect squares. In other words, both terms should have 2 as their exponent.
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m4-81 |
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= |
(m2)2-81 |
(m2)2=m4 |
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= |
(m2)2-92 |
92=81 |
Next, label the values in the expression (m2)2-92 and substitute the values into the formula given for Factoring the Difference of Two Squares.
a2−b2 |
= |
(a+b)(a−b) |
(m2)2−92 |
= |
(m2+9)(m2−9) |
Now, express both terms inside the second parenthesis as perfect squares. In other words, both terms should have 2 as their exponent.
Finally, label the values in the expression m2-32 and substitute the values into the formula given for Factoring the Difference of Two Squares.
a2−b2 |
= |
(a−b)(a+b) |
(m2+9)(m2−32) |
= |
(m2+9)(m−3)(m+3) |
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Question 4 of 4
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First, express both terms inside the parenthesis as perfect squares. In other words, both terms should have 2 as their exponent.
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16x4-1 |
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= |
(4x2)2-1 |
(4x2)2=16x4 |
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= |
(4x2)2-12 |
12=1 |
Next, label the values in the expression (4x2)2-12 and substitute the values into the formula given for Factoring the Difference of Two Squares.
a2−b2 |
= |
(a+b)(a−b) |
(4x2)2−12 |
= |
(4x2+1)(4x2−1) |
Now, express both terms inside the second parenthesis as perfect squares. In other words, both terms should have 2 as their exponent.
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4x2-1 |
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= |
(2x)2-1 |
(2x)2=4x2 |
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= |
(2x)2-12 |
12=1 |
Finally, label the values in the expression (2x)2-12 and substitute the values into the formula given for Factoring the Difference of Two Squares.
a2−b2 |
= |
(a−b)(a+b) |
(4x2+1)[(2x)2−12] |
= |
(4x2+1)(2x−1)(2x+1) |