Expand the Trigonometric Expression (5a-3b)^2

${(5 a - 3 b)}^{2}$

Step 1

Rewrite ${(5 a - 3 b)}^{2}$ as $(5 a - 3 b) (5 a - 3 b)$ .

$(5 a - 3 b) (5 a - 3 b)$

Step 2

Expand $(5 a - 3 b) (5 a - 3 b)$ using the FOIL Method.

Apply the distributive property.

$5 a (5 a - 3 b) - 3 b (5 a - 3 b)$

Apply the distributive property.

$5 a (5 a) + 5 a (- 3 b) - 3 b (5 a - 3 b)$

Apply the distributive property.

$5 a (5 a) + 5 a (- 3 b) - 3 b (5 a) - 3 b (- 3 b)$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$5 \cdot 5 a \cdot a + 5 a (- 3 b) - 3 b (5 a) - 3 b (- 3 b)$

Multiply $a$ by $a$ by adding the exponents.

Move $a$ .

$5 \cdot 5 (a \cdot a) + 5 a (- 3 b) - 3 b (5 a) - 3 b (- 3 b)$

Multiply $a$ by $a$ .

$5 \cdot 5 a^{2} + 5 a (- 3 b) - 3 b (5 a) - 3 b (- 3 b)$

Multiply $5$ by $5$ .

$25 a^{2} + 5 a (- 3 b) - 3 b (5 a) - 3 b (- 3 b)$

Rewrite using the commutative property of multiplication.

$25 a^{2} + 5 \cdot - 3 a b - 3 b (5 a) - 3 b (- 3 b)$

Multiply $5$ by $- 3$ .

$25 a^{2} - 15 a b - 3 b (5 a) - 3 b (- 3 b)$

Rewrite using the commutative property of multiplication.

$25 a^{2} - 15 a b - 3 \cdot 5 b a - 3 b (- 3 b)$

Multiply $- 3$ by $5$ .

$25 a^{2} - 15 a b - 15 b a - 3 b (- 3 b)$

Rewrite using the commutative property of multiplication.

$25 a^{2} - 15 a b - 15 b a - 3 \cdot - 3 b \cdot b$

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

Move $b$ .

$25 a^{2} - 15 a b - 15 b a - 3 \cdot - 3 (b \cdot b)$

Multiply $b$ by $b$ .

$25 a^{2} - 15 a b - 15 b a - 3 \cdot - 3 b^{2}$

Multiply $- 3$ by $- 3$ .

$25 a^{2} - 15 a b - 15 b a + 9 b^{2}$

Subtract $15 b a$ from $- 15 a b$ .

Move $b$ .

$25 a^{2} - 15 a b - 15 a b + 9 b^{2}$

Subtract $15 a b$ from $- 15 a b$ .

$25 a^{2} - 30 a b + 9 b^{2}$

Expand the Trigonometric Expression (5a-3b)^2

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