Basic Math Examples

$3 y (2 y + 2) - 5 y (3 y - 7)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$3 y (2 y) + 3 y \cdot 2 - 5 y (3 y - 7)$

Step 1.2

Rewrite using the commutative property of multiplication.

$3 \cdot 2 y \cdot y + 3 y \cdot 2 - 5 y (3 y - 7)$

Step 1.3

Multiply $2$ by $3$ .

$3 \cdot 2 y \cdot y + 6 y - 5 y (3 y - 7)$

Step 1.4

Simplify each term.

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Step 1.4.1

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

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Step 1.4.1.1

Move $y$ .

$3 \cdot 2 (y \cdot y) + 6 y - 5 y (3 y - 7)$

Step 1.4.1.2

Multiply $y$ by $y$ .

$3 \cdot 2 y^{2} + 6 y - 5 y (3 y - 7)$

Step 1.4.2

Multiply $3$ by $2$ .

$6 y^{2} + 6 y - 5 y (3 y - 7)$

Step 1.5

Apply the distributive property.

$6 y^{2} + 6 y - 5 y (3 y) - 5 y \cdot - 7$

Step 1.6

Rewrite using the commutative property of multiplication.

$6 y^{2} + 6 y - 5 \cdot 3 y \cdot y - 5 y \cdot - 7$

Step 1.7

Multiply $- 7$ by $- 5$ .

$6 y^{2} + 6 y - 5 \cdot 3 y \cdot y + 35 y$

Step 1.8

Simplify each term.

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Step 1.8.1

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

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Step 1.8.1.1

Move $y$ .

$6 y^{2} + 6 y - 5 \cdot 3 (y \cdot y) + 35 y$

Step 1.8.1.2

Multiply $y$ by $y$ .

$6 y^{2} + 6 y - 5 \cdot 3 y^{2} + 35 y$

Step 1.8.2

Multiply $- 5$ by $3$ .

$6 y^{2} + 6 y - 15 y^{2} + 35 y$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $15 y^{2}$ from $6 y^{2}$ .

$- 9 y^{2} + 6 y + 35 y$

Step 2.2

Add $6 y$ and $35 y$ .

$- 9 y^{2} + 41 y$