Basic Math Examples

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

Step 1

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

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.

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

Step 2.1.2

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

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Step 2.1.2.1

Move $y$ .

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

Step 2.1.2.2

Multiply $y$ by $y$ .

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

Step 2.1.3

Multiply $5$ by $2$ .

$(10 y^{2} + 5 y \cdot - 3 - 2 (2 y) - 2 \cdot - 3) (4 y + 3)$

Step 2.1.4

Multiply $- 3$ by $5$ .

$(10 y^{2} - 15 y - 2 (2 y) - 2 \cdot - 3) (4 y + 3)$

Step 2.1.5

Multiply $2$ by $- 2$ .

$(10 y^{2} - 15 y - 4 y - 2 \cdot - 3) (4 y + 3)$

Step 2.1.6

Multiply $- 2$ by $- 3$ .

$(10 y^{2} - 15 y - 4 y + 6) (4 y + 3)$

Step 2.2

Subtract $4 y$ from $- 15 y$ .

$(10 y^{2} - 19 y + 6) (4 y + 3)$

Step 3

Expand $(10 y^{2} - 19 y + 6) (4 y + 3)$ by multiplying each term in the first expression by each term in the second expression.

$10 y^{2} (4 y) + 10 y^{2} \cdot 3 - 19 y (4 y) - 19 y \cdot 3 + 6 (4 y) + 6 \cdot 3$

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.

$10 \cdot 4 y^{2} y + 10 y^{2} \cdot 3 - 19 y (4 y) - 19 y \cdot 3 + 6 (4 y) + 6 \cdot 3$

Step 4.1.2

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

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Step 4.1.2.1

Move $y$ .

$10 \cdot 4 (y \cdot y^{2}) + 10 y^{2} \cdot 3 - 19 y (4 y) - 19 y \cdot 3 + 6 (4 y) + 6 \cdot 3$

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 $1$ .

$10 \cdot 4 (y^{1} y^{2}) + 10 y^{2} \cdot 3 - 19 y (4 y) - 19 y \cdot 3 + 6 (4 y) + 6 \cdot 3$

Step 4.1.2.2.2

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

$10 \cdot 4 y^{1 + 2} + 10 y^{2} \cdot 3 - 19 y (4 y) - 19 y \cdot 3 + 6 (4 y) + 6 \cdot 3$

Step 4.1.2.3

Add $1$ and $2$ .

$10 \cdot 4 y^{3} + 10 y^{2} \cdot 3 - 19 y (4 y) - 19 y \cdot 3 + 6 (4 y) + 6 \cdot 3$

Step 4.1.3

Multiply $10$ by $4$ .

$40 y^{3} + 10 y^{2} \cdot 3 - 19 y (4 y) - 19 y \cdot 3 + 6 (4 y) + 6 \cdot 3$

Step 4.1.4

Multiply $3$ by $10$ .

$40 y^{3} + 30 y^{2} - 19 y (4 y) - 19 y \cdot 3 + 6 (4 y) + 6 \cdot 3$

Step 4.1.5

Rewrite using the commutative property of multiplication.

$40 y^{3} + 30 y^{2} - 19 \cdot 4 y \cdot y - 19 y \cdot 3 + 6 (4 y) + 6 \cdot 3$

Step 4.1.6

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

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Step 4.1.6.1

Move $y$ .

$40 y^{3} + 30 y^{2} - 19 \cdot 4 (y \cdot y) - 19 y \cdot 3 + 6 (4 y) + 6 \cdot 3$

Step 4.1.6.2

Multiply $y$ by $y$ .

$40 y^{3} + 30 y^{2} - 19 \cdot 4 y^{2} - 19 y \cdot 3 + 6 (4 y) + 6 \cdot 3$

Step 4.1.7

Multiply $- 19$ by $4$ .

$40 y^{3} + 30 y^{2} - 76 y^{2} - 19 y \cdot 3 + 6 (4 y) + 6 \cdot 3$

Step 4.1.8

Multiply $3$ by $- 19$ .

$40 y^{3} + 30 y^{2} - 76 y^{2} - 57 y + 6 (4 y) + 6 \cdot 3$

Step 4.1.9

Multiply $4$ by $6$ .

$40 y^{3} + 30 y^{2} - 76 y^{2} - 57 y + 24 y + 6 \cdot 3$

Step 4.1.10

Multiply $6$ by $3$ .

$40 y^{3} + 30 y^{2} - 76 y^{2} - 57 y + 24 y + 18$

Step 4.2

Simplify by adding terms.

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Step 4.2.1

Subtract $76 y^{2}$ from $30 y^{2}$ .

$40 y^{3} - 46 y^{2} - 57 y + 24 y + 18$

Step 4.2.2

Add $- 57 y$ and $24 y$ .

$40 y^{3} - 46 y^{2} - 33 y + 18$