Factor each polynomial. x2−8x+16−y2

Question

Factor each polynomial.  x2−8x+16−y2

Annie Gonzalez · Accepted Answer

Step 1
We need to factor the following polynomial

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

Step 2
The polynomial can be factored as following

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

Dabanka4v · Accepted Answer

Step 1
To find the factor of the given polynomial.
Step 2
Given information:

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

Step 3
Calculation:
Rewrite (8 x) as,

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

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

= \overset{A p p l y {(a - b)}^{2} f or μ l a}{\overset{⏞}{x^{2} - (2 \times 4 \times x) + 4^{2}}} - y^{2}

= {(x - 4)}^{2} - y^{2} [∵ {(a - b)}^{2} = a^{2} - 2 a b + 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)

Factor each polynomial. x^{2}-8x+16-y^{2}