Question

Directions : Factor each of the following Differences of two squares and write your answer together with solution​

Answer 1

$\huge \boxed{\mathfrak{Question} \downarrow}$

Factor each of the following differences of two squares and write your answer together with solution.

$\large \boxed{\mathbb{ANSWER\: WITH\: EXPLANATION} \downarrow}$

1. x² - 36

$\sf \: x ^ { 2 } - 36$

Rewrite $\sf\:x^{2}-36 as x^{2}-6^{2}$. The difference of squares can be factored using the rule:$\sf\: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.

$\boxed{ \boxed{ \bf\left(x-6\right)\left(x+6\right) }}$

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2. 49 - x²

$\sf \: 49 - x ^ { 2 }$

Rewrite 49-x² as 7²-x². The difference of squares can be factored using the rule: $\sf\:a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.

$\sf \: \left(7-x\right)\left(7+x\right)$

Reorder the terms.

$\boxed{ \boxed{ \bf\left(-x+7\right)\left(x+7\right) }}$

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3. 81 - c²

$\sf \: 81 - c ^ { 2 }$

Rewrite 81-c²as 9²-c². The difference of squares can be factored using the rule: $\sf\:a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.

$\sf\left(9-c\right)\left(9+c\right)$

Reorder the terms.

$\boxed{ \boxed{ \bf\left(-c+9\right)\left(c+9\right) }}$

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4. m²n² - 1

$\sf \: m ^ { 2 } n ^ { 2 } - 1$

Rewrite m²n² - 1 as $\sf\left(mn\right)^{2}-1^{2}$. The difference of squares can be factored using the rule: $\sf\:a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.

$\boxed{ \boxed{ \bf\left(mn-1\right)\left(mn+1\right) }}$

Answer 2

Step-by-step explanation:

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