Precalculus Examples

$(10 x^{4} y^{2} + 9 x^{3} y + 5 y) - (9 x^{4} y^{2} + 12 x^{3} y + 2 y - 3 x)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$10 x^{4} y^{2} + 9 x^{3} y + 5 y - (9 x^{4} y^{2}) - (12 x^{3} y) - (2 y) - (- 3 x)$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $9$ by $- 1$ .

$10 x^{4} y^{2} + 9 x^{3} y + 5 y - 9 (x^{4} y^{2}) - (12 x^{3} y) - (2 y) - (- 3 x)$

Step 1.2.2

Multiply $12$ by $- 1$ .

$10 x^{4} y^{2} + 9 x^{3} y + 5 y - 9 (x^{4} y^{2}) - 12 (x^{3} y) - (2 y) - (- 3 x)$

Step 1.2.3

Multiply $2$ by $- 1$ .

$10 x^{4} y^{2} + 9 x^{3} y + 5 y - 9 (x^{4} y^{2}) - 12 (x^{3} y) - 2 y - (- 3 x)$

Step 1.2.4

Multiply $- 3$ by $- 1$ .

$10 x^{4} y^{2} + 9 x^{3} y + 5 y - 9 (x^{4} y^{2}) - 12 (x^{3} y) - 2 y + 3 x$

Step 1.3

Remove parentheses.

$10 x^{4} y^{2} + 9 x^{3} y + 5 y - 9 x^{4} y^{2} - 12 x^{3} y - 2 y + 3 x$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $9 x^{4} y^{2}$ from $10 x^{4} y^{2}$ .

$1 x^{4} y^{2} + 9 x^{3} y + 5 y - 12 x^{3} y - 2 y + 3 x$

Step 2.2

Multiply $x^{4}$ by $1$ .

$x^{4} y^{2} + 9 x^{3} y + 5 y - 12 x^{3} y - 2 y + 3 x$

Step 2.3

Subtract $12 x^{3} y$ from $9 x^{3} y$ .

$x^{4} y^{2} - 3 x^{3} y + 5 y - 2 y + 3 x$

Step 2.4

Subtract $2 y$ from $5 y$ .

$x^{4} y^{2} - 3 x^{3} y + 3 y + 3 x$