Factor f(x)=-(x-7)^2+1

$f (x) = - {(x - 7)}^{2} + 1$

Step 1

Rewrite $1$ as $1^{2}$ .

$f (x) = - {(x - 7)}^{2} + 1^{2}$

Step 2

Reorder $- {(x - 7)}^{2}$ and $1^{2}$ .

$f (x) = 1^{2} - {(x - 7)}^{2}$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 1$ and $b = x - 7$ .

$f (x) = (1 + x - 7) (1 - (x - 7))$

Step 4

Simplify.

Subtract $7$ from $1$ .

$f (x) = (x - 6) (1 - (x - 7))$

Apply the distributive property.

$f (x) = (x - 6) (1 - x + 7)$

Multiply $- 1$ by $- 7$ .

$f (x) = (x - 6) (1 - x + 7)$

Add $1$ and $7$ .

$f (x) = (x - 6) (- x + 8)$

Factor f(x)=-(x-7)^2+1

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