Expand the Trigonometric Expression (3a-11b)^2

${(3 a - 11 b)}^{2}$

Step 1

Rewrite ${(3 a - 11 b)}^{2}$ as $(3 a - 11 b) (3 a - 11 b)$ .

$(3 a - 11 b) (3 a - 11 b)$

Step 2

Expand $(3 a - 11 b) (3 a - 11 b)$ using the FOIL Method.

Apply the distributive property.

$3 a (3 a - 11 b) - 11 b (3 a - 11 b)$

Apply the distributive property.

$3 a (3 a) + 3 a (- 11 b) - 11 b (3 a - 11 b)$

Apply the distributive property.

$3 a (3 a) + 3 a (- 11 b) - 11 b (3 a) - 11 b (- 11 b)$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$3 \cdot 3 a \cdot a + 3 a (- 11 b) - 11 b (3 a) - 11 b (- 11 b)$

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

Move $a$ .

$3 \cdot 3 (a \cdot a) + 3 a (- 11 b) - 11 b (3 a) - 11 b (- 11 b)$

Multiply $a$ by $a$ .

$3 \cdot 3 a^{2} + 3 a (- 11 b) - 11 b (3 a) - 11 b (- 11 b)$

Multiply $3$ by $3$ .

$9 a^{2} + 3 a (- 11 b) - 11 b (3 a) - 11 b (- 11 b)$

Rewrite using the commutative property of multiplication.

$9 a^{2} + 3 \cdot - 11 a b - 11 b (3 a) - 11 b (- 11 b)$

Multiply $3$ by $- 11$ .

$9 a^{2} - 33 a b - 11 b (3 a) - 11 b (- 11 b)$

Rewrite using the commutative property of multiplication.

$9 a^{2} - 33 a b - 11 \cdot 3 b a - 11 b (- 11 b)$

Multiply $- 11$ by $3$ .

$9 a^{2} - 33 a b - 33 b a - 11 b (- 11 b)$

Rewrite using the commutative property of multiplication.

$9 a^{2} - 33 a b - 33 b a - 11 \cdot - 11 b \cdot b$

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

Move $b$ .

$9 a^{2} - 33 a b - 33 b a - 11 \cdot - 11 (b \cdot b)$

Multiply $b$ by $b$ .

$9 a^{2} - 33 a b - 33 b a - 11 \cdot - 11 b^{2}$

Multiply $- 11$ by $- 11$ .

$9 a^{2} - 33 a b - 33 b a + 121 b^{2}$

Subtract $33 b a$ from $- 33 a b$ .

Move $b$ .

$9 a^{2} - 33 a b - 33 a b + 121 b^{2}$

Subtract $33 a b$ from $- 33 a b$ .

$9 a^{2} - 66 a b + 121 b^{2}$

Expand the Trigonometric Expression (3a-11b)^2

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