Evaluate (4+x)(4-x)

$(4 + x) (4 - x)$

Step 1

Expand $(4 + x) (4 - x)$ using the FOIL Method.

Apply the distributive property.

$4 (4 - x) + x (4 - x)$

Apply the distributive property.

$4 \cdot 4 + 4 (- x) + x (4 - x)$

Apply the distributive property.

$4 \cdot 4 + 4 (- x) + x \cdot 4 + x (- x)$

$4 \cdot 4 + 4 (- x) + x \cdot 4 + x (- x)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $4$ by $4$ .

$16 + 4 (- x) + x \cdot 4 + x (- x)$

Multiply $- 1$ by $4$ .

$16 - 4 x + x \cdot 4 + x (- x)$

Move $4$ to the left of $x$ .

$16 - 4 x + 4 \cdot x + x (- x)$

Rewrite using the commutative property of multiplication.

$16 - 4 x + 4 x - x \cdot x$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$16 - 4 x + 4 x - (x \cdot x)$

Multiply $x$ by $x$ .

$16 - 4 x + 4 x - x^{2}$

$16 - 4 x + 4 x - x^{2}$

$16 - 4 x + 4 x - x^{2}$

Add $- 4 x$ and $4 x$ .

$16 + 0 - x^{2}$

Add $16$ and $0$ .

$16 - x^{2}$

$16 - x^{2}$

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