Algebra Examples

$(7 y^{6}) {(2 y - 4)}^{2}$

Step 1

Rewrite ${(2 y - 4)}^{2}$ as $(2 y - 4) (2 y - 4)$ .

$7 y^{6} ((2 y - 4) (2 y - 4))$

Step 2

Expand $(2 y - 4) (2 y - 4)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$7 y^{6} (2 y (2 y - 4) - 4 (2 y - 4))$

Step 2.2

Apply the distributive property.

$7 y^{6} (2 y (2 y) + 2 y \cdot - 4 - 4 (2 y - 4))$

Step 2.3

Apply the distributive property.

$7 y^{6} (2 y (2 y) + 2 y \cdot - 4 - 4 (2 y) - 4 \cdot - 4)$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Rewrite using the commutative property of multiplication.

$7 y^{6} (2 \cdot 2 y \cdot y + 2 y \cdot - 4 - 4 (2 y) - 4 \cdot - 4)$

Step 3.1.2

Multiply $y$ by $y$ by adding the exponents.

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Step 3.1.2.1

Move $y$ .

$7 y^{6} (2 \cdot 2 (y \cdot y) + 2 y \cdot - 4 - 4 (2 y) - 4 \cdot - 4)$

Step 3.1.2.2

Multiply $y$ by $y$ .

$7 y^{6} (2 \cdot 2 y^{2} + 2 y \cdot - 4 - 4 (2 y) - 4 \cdot - 4)$

Step 3.1.3

Multiply $2$ by $2$ .

$7 y^{6} (4 y^{2} + 2 y \cdot - 4 - 4 (2 y) - 4 \cdot - 4)$

Step 3.1.4

Multiply $- 4$ by $2$ .

$7 y^{6} (4 y^{2} - 8 y - 4 (2 y) - 4 \cdot - 4)$

Step 3.1.5

Multiply $2$ by $- 4$ .

$7 y^{6} (4 y^{2} - 8 y - 8 y - 4 \cdot - 4)$

Step 3.1.6

Multiply $- 4$ by $- 4$ .

$7 y^{6} (4 y^{2} - 8 y - 8 y + 16)$

Step 3.2

Subtract $8 y$ from $- 8 y$ .

$7 y^{6} (4 y^{2} - 16 y + 16)$

Step 4

Apply the distributive property.

$7 y^{6} (4 y^{2}) + 7 y^{6} (- 16 y) + 7 y^{6} \cdot 16$

Step 5

Simplify.

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Step 5.1

Rewrite using the commutative property of multiplication.

$7 \cdot 4 y^{6} y^{2} + 7 y^{6} (- 16 y) + 7 y^{6} \cdot 16$

Step 5.2

Rewrite using the commutative property of multiplication.

$7 \cdot 4 y^{6} y^{2} + 7 \cdot - 16 y^{6} y + 7 y^{6} \cdot 16$

Step 5.3

Multiply $16$ by $7$ .

$7 \cdot 4 y^{6} y^{2} + 7 \cdot - 16 y^{6} y + 112 y^{6}$

Step 6

Simplify each term.

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Step 6.1

Multiply $y^{6}$ by $y^{2}$ by adding the exponents.

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Step 6.1.1

Move $y^{2}$ .

$7 \cdot 4 (y^{2} y^{6}) + 7 \cdot - 16 y^{6} y + 112 y^{6}$

Step 6.1.2

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

$7 \cdot 4 y^{2 + 6} + 7 \cdot - 16 y^{6} y + 112 y^{6}$

Step 6.1.3

Add $2$ and $6$ .

$7 \cdot 4 y^{8} + 7 \cdot - 16 y^{6} y + 112 y^{6}$

Step 6.2

Multiply $7$ by $4$ .

$28 y^{8} + 7 \cdot - 16 y^{6} y + 112 y^{6}$

Step 6.3

Multiply $y^{6}$ by $y$ by adding the exponents.

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Step 6.3.1

Move $y$ .

$28 y^{8} + 7 \cdot - 16 (y \cdot y^{6}) + 112 y^{6}$

Step 6.3.2

Multiply $y$ by $y^{6}$ .

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Step 6.3.2.1

Raise $y$ to the power of $1$ .

$28 y^{8} + 7 \cdot - 16 (y^{1} y^{6}) + 112 y^{6}$

Step 6.3.2.2

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

$28 y^{8} + 7 \cdot - 16 y^{1 + 6} + 112 y^{6}$

Step 6.3.3

Add $1$ and $6$ .

$28 y^{8} + 7 \cdot - 16 y^{7} + 112 y^{6}$

Step 6.4

Multiply $7$ by $- 16$ .

$28 y^{8} - 112 y^{7} + 112 y^{6}$