Algebra Examples

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

Step 1

Simplify terms.

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Step 1.1

Subtract $3 m^{2}$ from $5 m^{2}$ .

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

Step 1.2

Apply the distributive property.

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

Step 2

Expand $(2 m^{2} y + 6 y) (- 3 m + 2)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

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

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

Step 3

Simplify each term.

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Step 3.1

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

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Step 3.1.1

Move $m$ .

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

Step 3.1.2

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

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Step 3.1.2.1

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

$2 (m^{1} m^{2}) y \cdot - 3 + 2 m^{2} y \cdot 2 + 6 y (- 3 m) + 6 y \cdot 2$

Step 3.1.2.2

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

$2 m^{1 + 2} y \cdot - 3 + 2 m^{2} y \cdot 2 + 6 y (- 3 m) + 6 y \cdot 2$

Step 3.1.3

Add $1$ and $2$ .

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

Step 3.2

Multiply $- 3$ by $2$ .

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

Step 3.3

Multiply $2$ by $2$ .

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

Step 3.4

Rewrite using the commutative property of multiplication.

$- 6 m^{3} y + 4 m^{2} y + 6 \cdot - 3 y m + 6 y \cdot 2$

Step 3.5

Multiply $6$ by $- 3$ .

$- 6 m^{3} y + 4 m^{2} y - 18 y m + 6 y \cdot 2$

Step 3.6

Multiply $2$ by $6$ .

$- 6 m^{3} y + 4 m^{2} y - 18 y m + 12 y$