Expand the Trigonometric Expression (4y^a-6x^b)(4y^a+6x^b)

$(4 y^{a} - 6 x^{b}) (4 y^{a} + 6 x^{b})$

Step 1

Expand $(4 y^{a} - 6 x^{b}) (4 y^{a} + 6 x^{b})$ using the FOIL Method.

Apply the distributive property.

$4 y^{a} (4 y^{a} + 6 x^{b}) - 6 x^{b} (4 y^{a} + 6 x^{b})$

Apply the distributive property.

$4 y^{a} (4 y^{a}) + 4 y^{a} (6 x^{b}) - 6 x^{b} (4 y^{a} + 6 x^{b})$

Apply the distributive property.

$4 y^{a} (4 y^{a}) + 4 y^{a} (6 x^{b}) - 6 x^{b} (4 y^{a}) - 6 x^{b} (6 x^{b})$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$4 \cdot 4 y^{a} y^{a} + 4 y^{a} (6 x^{b}) - 6 x^{b} (4 y^{a}) - 6 x^{b} (6 x^{b})$

Multiply $y^{a}$ by $y^{a}$ by adding the exponents.

Move $y^{a}$ .

$4 \cdot 4 (y^{a} y^{a}) + 4 y^{a} (6 x^{b}) - 6 x^{b} (4 y^{a}) - 6 x^{b} (6 x^{b})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$4 \cdot 4 y^{a + a} + 4 y^{a} (6 x^{b}) - 6 x^{b} (4 y^{a}) - 6 x^{b} (6 x^{b})$

Add $a$ and $a$ .

$4 \cdot 4 y^{2 a} + 4 y^{a} (6 x^{b}) - 6 x^{b} (4 y^{a}) - 6 x^{b} (6 x^{b})$

Multiply $4$ by $4$ .

$16 y^{2 a} + 4 y^{a} (6 x^{b}) - 6 x^{b} (4 y^{a}) - 6 x^{b} (6 x^{b})$

Rewrite using the commutative property of multiplication.

$16 y^{2 a} + 4 \cdot 6 y^{a} x^{b} - 6 x^{b} (4 y^{a}) - 6 x^{b} (6 x^{b})$

Multiply $4$ by $6$ .

$16 y^{2 a} + 24 y^{a} x^{b} - 6 x^{b} (4 y^{a}) - 6 x^{b} (6 x^{b})$

Rewrite using the commutative property of multiplication.

$16 y^{2 a} + 24 y^{a} x^{b} - 6 \cdot 4 x^{b} y^{a} - 6 x^{b} (6 x^{b})$

Multiply $- 6$ by $4$ .

$16 y^{2 a} + 24 y^{a} x^{b} - 24 x^{b} y^{a} - 6 x^{b} (6 x^{b})$

Rewrite using the commutative property of multiplication.

$16 y^{2 a} + 24 y^{a} x^{b} - 24 x^{b} y^{a} - 6 \cdot 6 x^{b} x^{b}$

Multiply $x^{b}$ by $x^{b}$ by adding the exponents.

Move $x^{b}$ .

$16 y^{2 a} + 24 y^{a} x^{b} - 24 x^{b} y^{a} - 6 \cdot 6 (x^{b} x^{b})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$16 y^{2 a} + 24 y^{a} x^{b} - 24 x^{b} y^{a} - 6 \cdot 6 x^{b + b}$

Add $b$ and $b$ .

$16 y^{2 a} + 24 y^{a} x^{b} - 24 x^{b} y^{a} - 6 \cdot 6 x^{2 b}$

Multiply $- 6$ by $6$ .

$16 y^{2 a} + 24 y^{a} x^{b} - 24 x^{b} y^{a} - 36 x^{2 b}$

Subtract $24 x^{b} y^{a}$ from $24 y^{a} x^{b}$ .

Move $y^{a}$ .

$16 y^{2 a} + 24 x^{b} y^{a} - 24 x^{b} y^{a} - 36 x^{2 b}$

Subtract $24 x^{b} y^{a}$ from $24 x^{b} y^{a}$ .

$16 y^{2 a} + 0 - 36 x^{2 b}$

Add $16 y^{2 a}$ and $0$ .

$16 y^{2 a} - 36 x^{2 b}$

Expand the Trigonometric Expression (4y^a-6x^b)(4y^a+6x^b)

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