Find the Product (3x-8)^2

${(3 x - 8)}^{2}$

Step 1

Rewrite ${(3 x - 8)}^{2}$ as $(3 x - 8) (3 x - 8)$ .

$(3 x - 8) (3 x - 8)$

Step 2

Expand $(3 x - 8) (3 x - 8)$ using the FOIL Method.

Apply the distributive property.

$3 x (3 x - 8) - 8 (3 x - 8)$

Apply the distributive property.

$3 x (3 x) + 3 x \cdot - 8 - 8 (3 x - 8)$

Apply the distributive property.

$3 x (3 x) + 3 x \cdot - 8 - 8 (3 x) - 8 \cdot - 8$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$3 \cdot 3 x \cdot x + 3 x \cdot - 8 - 8 (3 x) - 8 \cdot - 8$

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

Move $x$ .

$3 \cdot 3 (x \cdot x) + 3 x \cdot - 8 - 8 (3 x) - 8 \cdot - 8$

Multiply $x$ by $x$ .

$3 \cdot 3 x^{2} + 3 x \cdot - 8 - 8 (3 x) - 8 \cdot - 8$

Multiply $3$ by $3$ .

$9 x^{2} + 3 x \cdot - 8 - 8 (3 x) - 8 \cdot - 8$

Multiply $- 8$ by $3$ .

$9 x^{2} - 24 x - 8 (3 x) - 8 \cdot - 8$

Multiply $3$ by $- 8$ .

$9 x^{2} - 24 x - 24 x - 8 \cdot - 8$

Multiply $- 8$ by $- 8$ .

$9 x^{2} - 24 x - 24 x + 64$

Subtract $24 x$ from $- 24 x$ .

$9 x^{2} - 48 x + 64$