Simplify (7x-4)^2

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

Step 1

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

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

Step 2

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $7$ by $7$ .

$49 x^{2} + 7 x \cdot - 4 - 4 (7 x) - 4 \cdot - 4$

Multiply $- 4$ by $7$ .

$49 x^{2} - 28 x - 4 (7 x) - 4 \cdot - 4$

Multiply $7$ by $- 4$ .

$49 x^{2} - 28 x - 28 x - 4 \cdot - 4$

Multiply $- 4$ by $- 4$ .

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

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

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