Simplify (2x-4)^2-(x+7)(x-2)

${(2 x - 4)}^{2} - (x + 7) (x - 2)$

Step 1

Simplify each term.

Rewrite ${(2 x - 4)}^{2}$ as $(2 x - 4) (2 x - 4)$ .

$(2 x - 4) (2 x - 4) - (x + 7) (x - 2)$

Expand $(2 x - 4) (2 x - 4)$ using the FOIL Method.

Apply the distributive property.

$2 x (2 x - 4) - 4 (2 x - 4) - (x + 7) (x - 2)$

Apply the distributive property.

$2 x (2 x) + 2 x \cdot - 4 - 4 (2 x - 4) - (x + 7) (x - 2)$

Apply the distributive property.

$2 x (2 x) + 2 x \cdot - 4 - 4 (2 x) - 4 \cdot - 4 - (x + 7) (x - 2)$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 2 x \cdot x + 2 x \cdot - 4 - 4 (2 x) - 4 \cdot - 4 - (x + 7) (x - 2)$

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

Move $x$ .

$2 \cdot 2 (x \cdot x) + 2 x \cdot - 4 - 4 (2 x) - 4 \cdot - 4 - (x + 7) (x - 2)$

Multiply $x$ by $x$ .

$2 \cdot 2 x^{2} + 2 x \cdot - 4 - 4 (2 x) - 4 \cdot - 4 - (x + 7) (x - 2)$

Multiply $2$ by $2$ .

$4 x^{2} + 2 x \cdot - 4 - 4 (2 x) - 4 \cdot - 4 - (x + 7) (x - 2)$

Multiply $- 4$ by $2$ .

$4 x^{2} - 8 x - 4 (2 x) - 4 \cdot - 4 - (x + 7) (x - 2)$

Multiply $2$ by $- 4$ .

$4 x^{2} - 8 x - 8 x - 4 \cdot - 4 - (x + 7) (x - 2)$

Multiply $- 4$ by $- 4$ .

$4 x^{2} - 8 x - 8 x + 16 - (x + 7) (x - 2)$

Subtract $8 x$ from $- 8 x$ .

$4 x^{2} - 16 x + 16 - (x + 7) (x - 2)$

Apply the distributive property.

$4 x^{2} - 16 x + 16 + (- x - 1 \cdot 7) (x - 2)$

Multiply $- 1$ by $7$ .

$4 x^{2} - 16 x + 16 + (- x - 7) (x - 2)$

Expand $(- x - 7) (x - 2)$ using the FOIL Method.

Apply the distributive property.

$4 x^{2} - 16 x + 16 - x (x - 2) - 7 (x - 2)$

Apply the distributive property.

$4 x^{2} - 16 x + 16 - x \cdot x - x \cdot - 2 - 7 (x - 2)$

Apply the distributive property.

$4 x^{2} - 16 x + 16 - x \cdot x - x \cdot - 2 - 7 x - 7 \cdot - 2$

Simplify and combine like terms.

Simplify each term.

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

Move $x$ .

$4 x^{2} - 16 x + 16 - (x \cdot x) - x \cdot - 2 - 7 x - 7 \cdot - 2$

Multiply $x$ by $x$ .

$4 x^{2} - 16 x + 16 - x^{2} - x \cdot - 2 - 7 x - 7 \cdot - 2$

Multiply $- 2$ by $- 1$ .

$4 x^{2} - 16 x + 16 - x^{2} + 2 x - 7 x - 7 \cdot - 2$

Multiply $- 7$ by $- 2$ .

$4 x^{2} - 16 x + 16 - x^{2} + 2 x - 7 x + 14$

Subtract $7 x$ from $2 x$ .

$4 x^{2} - 16 x + 16 - x^{2} - 5 x + 14$

Step 2

Simplify by adding terms.

Subtract $x^{2}$ from $4 x^{2}$ .

$3 x^{2} - 16 x + 16 - 5 x + 14$

Subtract $5 x$ from $- 16 x$ .

$3 x^{2} - 21 x + 16 + 14$

Add $16$ and $14$ .

$3 x^{2} - 21 x + 30$

Simplify (2x-4)^2-(x+7)(x-2)

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