Algebra Examples

$8 m (1 + 2 m) - (4 m + 3) (4 m - 3) = 2 m$

Step 1

Simplify $8 m (1 + 2 m) - (4 m + 3) (4 m - 3)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$8 m \cdot 1 + 8 m (2 m) - (4 m + 3) (4 m - 3) = 2 m$

Step 1.1.2

Multiply $8$ by $1$ .

$8 m + 8 m (2 m) - (4 m + 3) (4 m - 3) = 2 m$

Step 1.1.3

Rewrite using the commutative property of multiplication.

$8 m + 8 \cdot 2 m \cdot m - (4 m + 3) (4 m - 3) = 2 m$

Step 1.1.4

Simplify each term.

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Step 1.1.4.1

Multiply $m$ by $m$ by adding the exponents.

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Step 1.1.4.1.1

Move $m$ .

$8 m + 8 \cdot 2 (m \cdot m) - (4 m + 3) (4 m - 3) = 2 m$

Step 1.1.4.1.2

Multiply $m$ by $m$ .

$8 m + 8 \cdot 2 m^{2} - (4 m + 3) (4 m - 3) = 2 m$

Step 1.1.4.2

Multiply $8$ by $2$ .

$8 m + 16 m^{2} - (4 m + 3) (4 m - 3) = 2 m$

Step 1.1.5

Apply the distributive property.

$8 m + 16 m^{2} + (- (4 m) - 1 \cdot 3) (4 m - 3) = 2 m$

Step 1.1.6

Multiply $4$ by $- 1$ .

$8 m + 16 m^{2} + (- 4 m - 1 \cdot 3) (4 m - 3) = 2 m$

Step 1.1.7

Multiply $- 1$ by $3$ .

$8 m + 16 m^{2} + (- 4 m - 3) (4 m - 3) = 2 m$

Step 1.1.8

Expand $(- 4 m - 3) (4 m - 3)$ using the FOIL Method.

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Step 1.1.8.1

Apply the distributive property.

$8 m + 16 m^{2} - 4 m (4 m - 3) - 3 (4 m - 3) = 2 m$

Step 1.1.8.2

Apply the distributive property.

$8 m + 16 m^{2} - 4 m (4 m) - 4 m \cdot - 3 - 3 (4 m - 3) = 2 m$

Step 1.1.8.3

Apply the distributive property.

$8 m + 16 m^{2} - 4 m (4 m) - 4 m \cdot - 3 - 3 (4 m) - 3 \cdot - 3 = 2 m$

Step 1.1.9

Simplify and combine like terms.

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Step 1.1.9.1

Simplify each term.

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Step 1.1.9.1.1

Rewrite using the commutative property of multiplication.

$8 m + 16 m^{2} - 4 \cdot 4 m \cdot m - 4 m \cdot - 3 - 3 (4 m) - 3 \cdot - 3 = 2 m$

Step 1.1.9.1.2

Multiply $m$ by $m$ by adding the exponents.

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Step 1.1.9.1.2.1

Move $m$ .

$8 m + 16 m^{2} - 4 \cdot 4 (m \cdot m) - 4 m \cdot - 3 - 3 (4 m) - 3 \cdot - 3 = 2 m$

Step 1.1.9.1.2.2

Multiply $m$ by $m$ .

$8 m + 16 m^{2} - 4 \cdot 4 m^{2} - 4 m \cdot - 3 - 3 (4 m) - 3 \cdot - 3 = 2 m$

Step 1.1.9.1.3

Multiply $- 4$ by $4$ .

$8 m + 16 m^{2} - 16 m^{2} - 4 m \cdot - 3 - 3 (4 m) - 3 \cdot - 3 = 2 m$

Step 1.1.9.1.4

Multiply $- 3$ by $- 4$ .

$8 m + 16 m^{2} - 16 m^{2} + 12 m - 3 (4 m) - 3 \cdot - 3 = 2 m$

Step 1.1.9.1.5

Multiply $4$ by $- 3$ .

$8 m + 16 m^{2} - 16 m^{2} + 12 m - 12 m - 3 \cdot - 3 = 2 m$

Step 1.1.9.1.6

Multiply $- 3$ by $- 3$ .

$8 m + 16 m^{2} - 16 m^{2} + 12 m - 12 m + 9 = 2 m$

Step 1.1.9.2

Subtract $12 m$ from $12 m$ .

$8 m + 16 m^{2} - 16 m^{2} + 0 + 9 = 2 m$

Step 1.1.9.3

Add $- 16 m^{2}$ and $0$ .

$8 m + 16 m^{2} - 16 m^{2} + 9 = 2 m$

Step 1.2

Combine the opposite terms in $8 m + 16 m^{2} - 16 m^{2} + 9$ .

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Step 1.2.1

Subtract $16 m^{2}$ from $16 m^{2}$ .

$8 m + 0 + 9 = 2 m$

Step 1.2.2

Add $8 m$ and $0$ .

$8 m + 9 = 2 m$

Step 2

Move all terms containing $m$ to the left side of the equation.

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Step 2.1

Subtract $2 m$ from both sides of the equation.

$8 m + 9 - 2 m = 0$

Step 2.2

Subtract $2 m$ from $8 m$ .

$6 m + 9 = 0$

Step 3

Subtract $9$ from both sides of the equation.

$6 m = - 9$

Step 4

Divide each term in $6 m = - 9$ by $6$ and simplify.

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Step 4.1

Divide each term in $6 m = - 9$ by $6$ .

$\frac{6 m}{6} = \frac{- 9}{6}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $6$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{6 m}{6} = \frac{- 9}{6}$

Step 4.2.1.2

Divide $m$ by $1$ .

$m = \frac{- 9}{6}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Cancel the common factor of $- 9$ and $6$ .

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Step 4.3.1.1

Factor $3$ out of $- 9$ .

$m = \frac{3 (- 3)}{6}$

Step 4.3.1.2

Cancel the common factors.

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Step 4.3.1.2.1

Factor $3$ out of $6$ .

$m = \frac{3 \cdot - 3}{3 \cdot 2}$

Step 4.3.1.2.2

Cancel the common factor.

$m = \frac{3 \cdot - 3}{3 \cdot 2}$

Step 4.3.1.2.3

Rewrite the expression.

$m = \frac{- 3}{2}$

Step 4.3.2

Move the negative in front of the fraction.

$m = - \frac{3}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$m = - \frac{3}{2}$

Decimal Form:

$m = - 1.5$

Mixed Number Form:

$m = - 1 \frac{1}{2}$