Linear Algebra Examples

$(4 x^{5} - 9 x^{7} + 16) - (5 x^{5} + 25 x^{7} - 10)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$4 x^{5} - 9 x^{7} + 16 - (5 x^{5}) - (25 x^{7}) - - 10$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $5$ by $- 1$ .

$4 x^{5} - 9 x^{7} + 16 - 5 x^{5} - (25 x^{7}) - - 10$

Step 1.2.2

Multiply $25$ by $- 1$ .

$4 x^{5} - 9 x^{7} + 16 - 5 x^{5} - 25 x^{7} - - 10$

Step 1.2.3

Multiply $- 1$ by $- 10$ .

$4 x^{5} - 9 x^{7} + 16 - 5 x^{5} - 25 x^{7} + 10$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $5 x^{5}$ from $4 x^{5}$ .

$- x^{5} - 9 x^{7} + 16 - 25 x^{7} + 10$

Step 2.2

Subtract $25 x^{7}$ from $- 9 x^{7}$ .

$- x^{5} - 34 x^{7} + 16 + 10$

Step 2.3

Add $16$ and $10$ .

$- x^{5} - 34 x^{7} + 26$