Algebra Examples

$16 a^{2} - 32 a + 9$ from $12 a^{2} + 60 a - 8$

Step 1

Write the problem as a mathematical expression.

$12 a^{2} + 60 a - 8 - (16 a^{2} - 32 a + 9)$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$12 a^{2} + 60 a - 8 - (16 a^{2}) - (- 32 a) - 1 \cdot 9$

Step 2.2

Simplify.

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Step 2.2.1

Multiply $16$ by $- 1$ .

$12 a^{2} + 60 a - 8 - 16 a^{2} - (- 32 a) - 1 \cdot 9$

Step 2.2.2

Multiply $- 32$ by $- 1$ .

$12 a^{2} + 60 a - 8 - 16 a^{2} + 32 a - 1 \cdot 9$

Step 2.2.3

Multiply $- 1$ by $9$ .

$12 a^{2} + 60 a - 8 - 16 a^{2} + 32 a - 9$

Step 3

Simplify by adding terms.

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Step 3.1

Subtract $16 a^{2}$ from $12 a^{2}$ .

$- 4 a^{2} + 60 a - 8 + 32 a - 9$

Step 3.2

Add $60 a$ and $32 a$ .

$- 4 a^{2} + 92 a - 8 - 9$

Step 3.3

Subtract $9$ from $- 8$ .

$- 4 a^{2} + 92 a - 17$