Basic Math Examples

$(4 y + 5) (7 y^{2} - 3 y - 2)$

Step 1

Expand

$(4 y + 5) (7 y^{2} - 3 y - 2)$ by multiplying each term in the first expression by each term in the second expression.

$4 y (7 y^{2}) + 4 y (- 3 y) + 4 y \cdot - 2 + 5 (7 y^{2}) + 5 (- 3 y) + 5 \cdot - 2$

Step 2

Simplify 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.

$4 \cdot 7 y \cdot y^{2} + 4 y (- 3 y) + 4 y \cdot - 2 + 5 (7 y^{2}) + 5 (- 3 y) + 5 \cdot - 2$

Step 2.1.2

Multiply

$y$ by

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

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Step 2.1.2.1

Move

$y^{2}$ .

$4 \cdot 7 (y^{2} y) + 4 y (- 3 y) + 4 y \cdot - 2 + 5 (7 y^{2}) + 5 (- 3 y) + 5 \cdot - 2$

Step 2.1.2.2

Multiply

$y^{2}$ by

$y$ .

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Step 2.1.2.2.1

Raise

$y$ to the power of

$1$ .

$4 \cdot 7 (y^{2} y^{1}) + 4 y (- 3 y) + 4 y \cdot - 2 + 5 (7 y^{2}) + 5 (- 3 y) + 5 \cdot - 2$

Step 2.1.2.2.2

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$4 \cdot 7 y^{2 + 1} + 4 y (- 3 y) + 4 y \cdot - 2 + 5 (7 y^{2}) + 5 (- 3 y) + 5 \cdot - 2$

Step 2.1.2.3

Add

$2$ and

$1$ .

$4 \cdot 7 y^{3} + 4 y (- 3 y) + 4 y \cdot - 2 + 5 (7 y^{2}) + 5 (- 3 y) + 5 \cdot - 2$

Step 2.1.3

Multiply

$4$ by

$7$ .

$28 y^{3} + 4 y (- 3 y) + 4 y \cdot - 2 + 5 (7 y^{2}) + 5 (- 3 y) + 5 \cdot - 2$

Step 2.1.4

Rewrite using the commutative property of multiplication.

$28 y^{3} + 4 \cdot - 3 y \cdot y + 4 y \cdot - 2 + 5 (7 y^{2}) + 5 (- 3 y) + 5 \cdot - 2$

Step 2.1.5

Multiply

$y$ by

$y$ by adding the exponents.

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Step 2.1.5.1

Move

$y$ .

$28 y^{3} + 4 \cdot - 3 (y \cdot y) + 4 y \cdot - 2 + 5 (7 y^{2}) + 5 (- 3 y) + 5 \cdot - 2$

Step 2.1.5.2

Multiply

$y$ by

$y$ .

$28 y^{3} + 4 \cdot - 3 y^{2} + 4 y \cdot - 2 + 5 (7 y^{2}) + 5 (- 3 y) + 5 \cdot - 2$

Step 2.1.6

Multiply

$4$ by

$- 3$ .

$28 y^{3} - 12 y^{2} + 4 y \cdot - 2 + 5 (7 y^{2}) + 5 (- 3 y) + 5 \cdot - 2$

Step 2.1.7

Multiply

$- 2$ by

$4$ .

$28 y^{3} - 12 y^{2} - 8 y + 5 (7 y^{2}) + 5 (- 3 y) + 5 \cdot - 2$

Step 2.1.8

Multiply

$7$ by

$5$ .

$28 y^{3} - 12 y^{2} - 8 y + 35 y^{2} + 5 (- 3 y) + 5 \cdot - 2$

Step 2.1.9

Multiply

$- 3$ by

$5$ .

$28 y^{3} - 12 y^{2} - 8 y + 35 y^{2} - 15 y + 5 \cdot - 2$

Step 2.1.10

Multiply

$5$ by

$- 2$ .

$28 y^{3} - 12 y^{2} - 8 y + 35 y^{2} - 15 y - 10$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Add

$- 12 y^{2}$ and

$35 y^{2}$ .

$28 y^{3} + 23 y^{2} - 8 y - 15 y - 10$

Step 2.2.2

Subtract

$15 y$ from

$- 8 y$ .

$28 y^{3} + 23 y^{2} - 23 y - 10$