Simplify (4x-7)^2

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

Step 1

Rewrite ${(4 x - 7)}^{2}$ as $(4 x - 7) (4 x - 7)$ .

$(4 x - 7) (4 x - 7)$

Step 2

Expand $(4 x - 7) (4 x - 7)$ using the FOIL Method.

Apply the distributive property.

$4 x (4 x - 7) - 7 (4 x - 7)$

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $4$ by $4$ .

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

Multiply $- 7$ by $4$ .

$16 x^{2} - 28 x - 7 (4 x) - 7 \cdot - 7$

Multiply $4$ by $- 7$ .

$16 x^{2} - 28 x - 28 x - 7 \cdot - 7$

Multiply $- 7$ by $- 7$ .

$16 x^{2} - 28 x - 28 x + 49$

Subtract $28 x$ from $- 28 x$ .

$16 x^{2} - 56 x + 49$