Expand the Trigonometric Expression (5b-7)^2

${(5 b - 7)}^{2}$

Step 1

Rewrite ${(5 b - 7)}^{2}$ as $(5 b - 7) (5 b - 7)$ .

$(5 b - 7) (5 b - 7)$

Step 2

Expand $(5 b - 7) (5 b - 7)$ using the FOIL Method.

Apply the distributive property.

$5 b (5 b - 7) - 7 (5 b - 7)$

Apply the distributive property.

$5 b (5 b) + 5 b \cdot - 7 - 7 (5 b - 7)$

Apply the distributive property.

$5 b (5 b) + 5 b \cdot - 7 - 7 (5 b) - 7 \cdot - 7$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$5 \cdot 5 b \cdot b + 5 b \cdot - 7 - 7 (5 b) - 7 \cdot - 7$

Multiply $b$ by $b$ by adding the exponents.

Move $b$ .

$5 \cdot 5 (b \cdot b) + 5 b \cdot - 7 - 7 (5 b) - 7 \cdot - 7$

Multiply $b$ by $b$ .

$5 \cdot 5 b^{2} + 5 b \cdot - 7 - 7 (5 b) - 7 \cdot - 7$

Multiply $5$ by $5$ .

$25 b^{2} + 5 b \cdot - 7 - 7 (5 b) - 7 \cdot - 7$

Multiply $- 7$ by $5$ .

$25 b^{2} - 35 b - 7 (5 b) - 7 \cdot - 7$

Multiply $5$ by $- 7$ .

$25 b^{2} - 35 b - 35 b - 7 \cdot - 7$

Multiply $- 7$ by $- 7$ .

$25 b^{2} - 35 b - 35 b + 49$

Subtract $35 b$ from $- 35 b$ .

$25 b^{2} - 70 b + 49$