Find the Product (-6x-7y^2)^2

${(- 6 x - 7 y^{2})}^{2}$

Step 1

Rewrite ${(- 6 x - 7 y^{2})}^{2}$ as $(- 6 x - 7 y^{2}) (- 6 x - 7 y^{2})$ .

$(- 6 x - 7 y^{2}) (- 6 x - 7 y^{2})$

Step 2

Expand $(- 6 x - 7 y^{2}) (- 6 x - 7 y^{2})$ using the FOIL Method.

Apply the distributive property.

$- 6 x (- 6 x - 7 y^{2}) - 7 y^{2} (- 6 x - 7 y^{2})$

Apply the distributive property.

$- 6 x (- 6 x) - 6 x (- 7 y^{2}) - 7 y^{2} (- 6 x - 7 y^{2})$

Apply the distributive property.

$- 6 x (- 6 x) - 6 x (- 7 y^{2}) - 7 y^{2} (- 6 x) - 7 y^{2} (- 7 y^{2})$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$- 6 \cdot - 6 x \cdot x - 6 x (- 7 y^{2}) - 7 y^{2} (- 6 x) - 7 y^{2} (- 7 y^{2})$

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

Move $x$ .

$- 6 \cdot - 6 (x \cdot x) - 6 x (- 7 y^{2}) - 7 y^{2} (- 6 x) - 7 y^{2} (- 7 y^{2})$

Multiply $x$ by $x$ .

$- 6 \cdot - 6 x^{2} - 6 x (- 7 y^{2}) - 7 y^{2} (- 6 x) - 7 y^{2} (- 7 y^{2})$

Multiply $- 6$ by $- 6$ .

$36 x^{2} - 6 x (- 7 y^{2}) - 7 y^{2} (- 6 x) - 7 y^{2} (- 7 y^{2})$

Rewrite using the commutative property of multiplication.

$36 x^{2} - 6 \cdot - 7 x y^{2} - 7 y^{2} (- 6 x) - 7 y^{2} (- 7 y^{2})$

Multiply $- 6$ by $- 7$ .

$36 x^{2} + 42 x y^{2} - 7 y^{2} (- 6 x) - 7 y^{2} (- 7 y^{2})$

Rewrite using the commutative property of multiplication.

$36 x^{2} + 42 x y^{2} - 7 \cdot - 6 y^{2} x - 7 y^{2} (- 7 y^{2})$

Multiply $- 7$ by $- 6$ .

$36 x^{2} + 42 x y^{2} + 42 y^{2} x - 7 y^{2} (- 7 y^{2})$

Rewrite using the commutative property of multiplication.

$36 x^{2} + 42 x y^{2} + 42 y^{2} x - 7 \cdot - 7 y^{2} y^{2}$

Multiply $y^{2}$ by $y^{2}$ by adding the exponents.

Move $y^{2}$ .

$36 x^{2} + 42 x y^{2} + 42 y^{2} x - 7 \cdot - 7 (y^{2} y^{2})$

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

$36 x^{2} + 42 x y^{2} + 42 y^{2} x - 7 \cdot - 7 y^{2 + 2}$

Add $2$ and $2$ .

$36 x^{2} + 42 x y^{2} + 42 y^{2} x - 7 \cdot - 7 y^{4}$

Multiply $- 7$ by $- 7$ .

$36 x^{2} + 42 x y^{2} + 42 y^{2} x + 49 y^{4}$

Add $42 x y^{2}$ and $42 y^{2} x$ .

Move $y^{2}$ .

$36 x^{2} + 42 x y^{2} + 42 x y^{2} + 49 y^{4}$

Add $42 x y^{2}$ and $42 x y^{2}$ .

$36 x^{2} + 84 x y^{2} + 49 y^{4}$

Find the Product (-6x-7y^2)^2

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