Sapewa

2021-12-15

Factor each polynomial.

$x}^{2}-8x+16-{y}^{2$

Annie Gonzalez

Beginner2021-12-16Added 41 answers

Step 1

We need to factor the following polynomial

$x}^{2}-8x+16-{y}^{2$

Step 2

The polynomial can be factored as following

$x}^{2}-8x+16-{y}^{2}=({x}^{2}-8x+16)-{y}^{2$

$={(x-4)}^{2}-{y}^{2}$

=[(x-4)-y][(x-4)+y] Using formula${a}^{2}-{b}^{2}=(a-b)(a+b)$

=(x-4-y)(x-4+y)

Hence,

${x}^{2}-8x+16-{y}^{2}=(x-4-y)(x-4+y)$

We need to factor the following polynomial

Step 2

The polynomial can be factored as following

=[(x-4)-y][(x-4)+y] Using formula

=(x-4-y)(x-4+y)

Hence,

Dabanka4v

Beginner2021-12-17Added 36 answers

Step 1

To find the factor of the given polynomial.

Step 2

Given information:

$x}^{2}-8x+16-{y}^{2$

Step 3

Calculation:

Rewrite (8 x) as,

$x}^{2}-8x+16-{y}^{2$

$={x}^{2}-(2\times 4\times x)+16-{y}^{2}$

$=\stackrel{Apply\text{}{(a-b)}^{2}\text{}f{\textstyle \phantom{\rule{1em}{0ex}}}\text{or}{\textstyle \phantom{\rule{1em}{0ex}}}\mu la}{\stackrel{\u23de}{{x}^{2}-(2\times 4\times x)+{4}^{2}}}-{y}^{2}$

$={(x-4)}^{2}-{y}^{2}\text{}\text{}\text{}[\because {(a-b)}^{2}={a}^{2}-2ab+{b}^{2}]$

Apply the formula$({a}^{2}-{b}^{2})=(a-b)(a+b)$ .

So,

$(x-4)}^{2}-{y}^{2$

=(x-4+y)(x-4-y)

Step 4

Thus, the factor of the given polynomial is

(x-4+y)(x-4-y)

To find the factor of the given polynomial.

Step 2

Given information:

Step 3

Calculation:

Rewrite (8 x) as,

Apply the formula

So,

=(x-4+y)(x-4-y)

Step 4

Thus, the factor of the given polynomial is

(x-4+y)(x-4-y)

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