Simplify (6x-7)^2

${(6 x - 7)}^{2}$

Step 1

Rewrite ${(6 x - 7)}^{2}$ as $(6 x - 7) (6 x - 7)$ .

$(6 x - 7) (6 x - 7)$

Step 2

Expand $(6 x - 7) (6 x - 7)$ using the FOIL Method.

Apply the distributive property.

$6 x (6 x - 7) - 7 (6 x - 7)$

Apply the distributive property.

$6 x (6 x) + 6 x \cdot - 7 - 7 (6 x - 7)$

Apply the distributive property.

$6 x (6 x) + 6 x \cdot - 7 - 7 (6 x) - 7 \cdot - 7$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$6 \cdot 6 x \cdot x + 6 x \cdot - 7 - 7 (6 x) - 7 \cdot - 7$

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

Move $x$ .

$6 \cdot 6 (x \cdot x) + 6 x \cdot - 7 - 7 (6 x) - 7 \cdot - 7$

Multiply $x$ by $x$ .

$6 \cdot 6 x^{2} + 6 x \cdot - 7 - 7 (6 x) - 7 \cdot - 7$

Multiply $6$ by $6$ .

$36 x^{2} + 6 x \cdot - 7 - 7 (6 x) - 7 \cdot - 7$

Multiply $- 7$ by $6$ .

$36 x^{2} - 42 x - 7 (6 x) - 7 \cdot - 7$

Multiply $6$ by $- 7$ .

$36 x^{2} - 42 x - 42 x - 7 \cdot - 7$

Multiply $- 7$ by $- 7$ .

$36 x^{2} - 42 x - 42 x + 49$

Subtract $42 x$ from $- 42 x$ .

$36 x^{2} - 84 x + 49$