Algebra Examples

$(3 y - 4) (5 y + 2) (2 y - 1)$

Step 1

Expand $(3 y - 4) (5 y + 2)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$(3 y (5 y + 2) - 4 (5 y + 2)) (2 y - 1)$

Step 1.2

Apply the distributive property.

$(3 y (5 y) + 3 y \cdot 2 - 4 (5 y + 2)) (2 y - 1)$

Step 1.3

Apply the distributive property.

$(3 y (5 y) + 3 y \cdot 2 - 4 (5 y) - 4 \cdot 2) (2 y - 1)$

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Rewrite using the commutative property of multiplication.

$(3 \cdot 5 y \cdot y + 3 y \cdot 2 - 4 (5 y) - 4 \cdot 2) (2 y - 1)$

Step 2.1.2

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

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Step 2.1.2.1

Move $y$ .

$(3 \cdot 5 (y \cdot y) + 3 y \cdot 2 - 4 (5 y) - 4 \cdot 2) (2 y - 1)$

Step 2.1.2.2

Multiply $y$ by $y$ .

$(3 \cdot 5 y^{2} + 3 y \cdot 2 - 4 (5 y) - 4 \cdot 2) (2 y - 1)$

Step 2.1.3

Multiply $3$ by $5$ .

$(15 y^{2} + 3 y \cdot 2 - 4 (5 y) - 4 \cdot 2) (2 y - 1)$

Step 2.1.4

Multiply $2$ by $3$ .

$(15 y^{2} + 6 y - 4 (5 y) - 4 \cdot 2) (2 y - 1)$

Step 2.1.5

Multiply $5$ by $- 4$ .

$(15 y^{2} + 6 y - 20 y - 4 \cdot 2) (2 y - 1)$

Step 2.1.6

Multiply $- 4$ by $2$ .

$(15 y^{2} + 6 y - 20 y - 8) (2 y - 1)$

Step 2.2

Subtract $20 y$ from $6 y$ .

$(15 y^{2} - 14 y - 8) (2 y - 1)$

Step 3

Expand $(15 y^{2} - 14 y - 8) (2 y - 1)$ by multiplying each term in the first expression by each term in the second expression.

$15 y^{2} (2 y) + 15 y^{2} \cdot - 1 - 14 y (2 y) - 14 y \cdot - 1 - 8 (2 y) - 8 \cdot - 1$

Step 4

Simplify terms.

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Step 4.1

Simplify each term.

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Step 4.1.1

Rewrite using the commutative property of multiplication.

$15 \cdot 2 y^{2} y + 15 y^{2} \cdot - 1 - 14 y (2 y) - 14 y \cdot - 1 - 8 (2 y) - 8 \cdot - 1$

Step 4.1.2

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

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Step 4.1.2.1

Move $y$ .

$15 \cdot 2 (y \cdot y^{2}) + 15 y^{2} \cdot - 1 - 14 y (2 y) - 14 y \cdot - 1 - 8 (2 y) - 8 \cdot - 1$

Step 4.1.2.2

Multiply $y$ by $y^{2}$ .

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Step 4.1.2.2.1

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

$15 \cdot 2 (y^{1} y^{2}) + 15 y^{2} \cdot - 1 - 14 y (2 y) - 14 y \cdot - 1 - 8 (2 y) - 8 \cdot - 1$

Step 4.1.2.2.2

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

$15 \cdot 2 y^{1 + 2} + 15 y^{2} \cdot - 1 - 14 y (2 y) - 14 y \cdot - 1 - 8 (2 y) - 8 \cdot - 1$

Step 4.1.2.3

Add $1$ and $2$ .

$15 \cdot 2 y^{3} + 15 y^{2} \cdot - 1 - 14 y (2 y) - 14 y \cdot - 1 - 8 (2 y) - 8 \cdot - 1$

Step 4.1.3

Multiply $15$ by $2$ .

$30 y^{3} + 15 y^{2} \cdot - 1 - 14 y (2 y) - 14 y \cdot - 1 - 8 (2 y) - 8 \cdot - 1$

Step 4.1.4

Multiply $- 1$ by $15$ .

$30 y^{3} - 15 y^{2} - 14 y (2 y) - 14 y \cdot - 1 - 8 (2 y) - 8 \cdot - 1$

Step 4.1.5

Rewrite using the commutative property of multiplication.

$30 y^{3} - 15 y^{2} - 14 \cdot 2 y \cdot y - 14 y \cdot - 1 - 8 (2 y) - 8 \cdot - 1$

Step 4.1.6

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

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Step 4.1.6.1

Move $y$ .

$30 y^{3} - 15 y^{2} - 14 \cdot 2 (y \cdot y) - 14 y \cdot - 1 - 8 (2 y) - 8 \cdot - 1$

Step 4.1.6.2

Multiply $y$ by $y$ .

$30 y^{3} - 15 y^{2} - 14 \cdot 2 y^{2} - 14 y \cdot - 1 - 8 (2 y) - 8 \cdot - 1$

Step 4.1.7

Multiply $- 14$ by $2$ .

$30 y^{3} - 15 y^{2} - 28 y^{2} - 14 y \cdot - 1 - 8 (2 y) - 8 \cdot - 1$

Step 4.1.8

Multiply $- 1$ by $- 14$ .

$30 y^{3} - 15 y^{2} - 28 y^{2} + 14 y - 8 (2 y) - 8 \cdot - 1$

Step 4.1.9

Multiply $2$ by $- 8$ .

$30 y^{3} - 15 y^{2} - 28 y^{2} + 14 y - 16 y - 8 \cdot - 1$

Step 4.1.10

Multiply $- 8$ by $- 1$ .

$30 y^{3} - 15 y^{2} - 28 y^{2} + 14 y - 16 y + 8$

Step 4.2

Simplify by adding terms.

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Step 4.2.1

Subtract $28 y^{2}$ from $- 15 y^{2}$ .

$30 y^{3} - 43 y^{2} + 14 y - 16 y + 8$

Step 4.2.2

Subtract $16 y$ from $14 y$ .

$30 y^{3} - 43 y^{2} - 2 y + 8$