Algebra Examples

${(y + 4)}^{3} - 2 y (y - 1)$

Step 1

Simplify each term.

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Step 1.1

Use the Binomial Theorem.

$y^{3} + 3 y^{2} \cdot 4 + 3 y \cdot 4^{2} + 4^{3} - 2 y (y - 1)$

Step 1.2

Simplify each term.

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Step 1.2.1

Multiply $4$ by $3$ .

$y^{3} + 12 y^{2} + 3 y \cdot 4^{2} + 4^{3} - 2 y (y - 1)$

Step 1.2.2

Raise $4$ to the power of $2$ .

$y^{3} + 12 y^{2} + 3 y \cdot 16 + 4^{3} - 2 y (y - 1)$

Step 1.2.3

Multiply $16$ by $3$ .

$y^{3} + 12 y^{2} + 48 y + 4^{3} - 2 y (y - 1)$

Step 1.2.4

Raise $4$ to the power of $3$ .

$y^{3} + 12 y^{2} + 48 y + 64 - 2 y (y - 1)$

Step 1.3

Apply the distributive property.

$y^{3} + 12 y^{2} + 48 y + 64 - 2 y \cdot y - 2 y \cdot - 1$

Step 1.4

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

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Step 1.4.1

Move $y$ .

$y^{3} + 12 y^{2} + 48 y + 64 - 2 (y \cdot y) - 2 y \cdot - 1$

Step 1.4.2

Multiply $y$ by $y$ .

$y^{3} + 12 y^{2} + 48 y + 64 - 2 y^{2} - 2 y \cdot - 1$

Step 1.5

Multiply $- 1$ by $- 2$ .

$y^{3} + 12 y^{2} + 48 y + 64 - 2 y^{2} + 2 y$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $2 y^{2}$ from $12 y^{2}$ .

$y^{3} + 10 y^{2} + 48 y + 64 + 2 y$

Step 2.2

Add $48 y$ and $2 y$ .

$y^{3} + 10 y^{2} + 50 y + 64$