Simplify (2x-7)^2

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

Step 1

Rewrite ${(2 x - 7)}^{2}$ as $(2 x - 7) (2 x - 7)$ .

$(2 x - 7) (2 x - 7)$

Step 2

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

Apply the distributive property.

$2 x (2 x - 7) - 7 (2 x - 7)$

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $2$ by $2$ .

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

Multiply $- 7$ by $2$ .

$4 x^{2} - 14 x - 7 (2 x) - 7 \cdot - 7$

Multiply $2$ by $- 7$ .

$4 x^{2} - 14 x - 14 x - 7 \cdot - 7$

Multiply $- 7$ by $- 7$ .

$4 x^{2} - 14 x - 14 x + 49$

Subtract $14 x$ from $- 14 x$ .

$4 x^{2} - 28 x + 49$