Basic Math Examples

$(9 a^{4} + 2 a^{2} + 5) - (16 a^{4} - 7 a^{2} + 1)$

Step 1

Apply the distributive property.

$9 a^{4} + 2 a^{2} + 5 - (16 a^{4}) - (- 7 a^{2}) - 1 \cdot 1$

Step 2

Simplify.

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Step 2.1

Multiply $16$ by $- 1$ .

$9 a^{4} + 2 a^{2} + 5 - 16 a^{4} - (- 7 a^{2}) - 1 \cdot 1$

Step 2.2

Multiply $- 7$ by $- 1$ .

$9 a^{4} + 2 a^{2} + 5 - 16 a^{4} + 7 a^{2} - 1 \cdot 1$

Step 2.3

Multiply $- 1$ by $1$ .

$9 a^{4} + 2 a^{2} + 5 - 16 a^{4} + 7 a^{2} - 1$

Step 3

Subtract $16 a^{4}$ from $9 a^{4}$ .

$- 7 a^{4} + 2 a^{2} + 5 + 7 a^{2} - 1$

Step 4

Add $2 a^{2}$ and $7 a^{2}$ .

$- 7 a^{4} + 9 a^{2} + 5 - 1$

Step 5

Subtract $1$ from $5$ .

$- 7 a^{4} + 9 a^{2} + 4$

Step 6

Factor $- 1$ out of $- 7 a^{4} + 9 a^{2} + 4$ .

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Step 6.1

Factor $- 1$ out of $- 7 a^{4}$ .

$- (7 a^{4}) + 9 a^{2} + 4$

Step 6.2

Factor $- 1$ out of $9 a^{2}$ .

$- (7 a^{4}) - (- 9 a^{2}) + 4$

Step 6.3

Rewrite $4$ as $- 1 (- 4)$ .

$- (7 a^{4}) - (- 9 a^{2}) - 1 (- 4)$

Step 6.4

Factor $- 1$ out of $- (7 a^{4}) - (- 9 a^{2})$ .

$- (7 a^{4} - 9 a^{2}) - 1 (- 4)$

Step 6.5

Factor $- 1$ out of $- (7 a^{4} - 9 a^{2}) - 1 (- 4)$ .

$- (7 a^{4} - 9 a^{2} - 4)$