Basic Math Examples

$9 h^{2} - (2 h + 3) (4 h - 5)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$9 h^{2} + (- (2 h) - 1 \cdot 3) (4 h - 5)$

Step 1.2

Multiply $2$ by $- 1$ .

$9 h^{2} + (- 2 h - 1 \cdot 3) (4 h - 5)$

Step 1.3

Multiply $- 1$ by $3$ .

$9 h^{2} + (- 2 h - 3) (4 h - 5)$

Step 1.4

Expand $(- 2 h - 3) (4 h - 5)$ using the FOIL Method.

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Step 1.4.1

Apply the distributive property.

$9 h^{2} - 2 h (4 h - 5) - 3 (4 h - 5)$

Step 1.4.2

Apply the distributive property.

$9 h^{2} - 2 h (4 h) - 2 h \cdot - 5 - 3 (4 h - 5)$

Step 1.4.3

Apply the distributive property.

$9 h^{2} - 2 h (4 h) - 2 h \cdot - 5 - 3 (4 h) - 3 \cdot - 5$

Step 1.5

Simplify and combine like terms.

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Step 1.5.1

Simplify each term.

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Step 1.5.1.1

Rewrite using the commutative property of multiplication.

$9 h^{2} - 2 \cdot 4 h \cdot h - 2 h \cdot - 5 - 3 (4 h) - 3 \cdot - 5$

Step 1.5.1.2

Multiply $h$ by $h$ by adding the exponents.

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Step 1.5.1.2.1

Move $h$ .

$9 h^{2} - 2 \cdot 4 (h \cdot h) - 2 h \cdot - 5 - 3 (4 h) - 3 \cdot - 5$

Step 1.5.1.2.2

Multiply $h$ by $h$ .

$9 h^{2} - 2 \cdot 4 h^{2} - 2 h \cdot - 5 - 3 (4 h) - 3 \cdot - 5$

Step 1.5.1.3

Multiply $- 2$ by $4$ .

$9 h^{2} - 8 h^{2} - 2 h \cdot - 5 - 3 (4 h) - 3 \cdot - 5$

Step 1.5.1.4

Multiply $- 5$ by $- 2$ .

$9 h^{2} - 8 h^{2} + 10 h - 3 (4 h) - 3 \cdot - 5$

Step 1.5.1.5

Multiply $4$ by $- 3$ .

$9 h^{2} - 8 h^{2} + 10 h - 12 h - 3 \cdot - 5$

Step 1.5.1.6

Multiply $- 3$ by $- 5$ .

$9 h^{2} - 8 h^{2} + 10 h - 12 h + 15$

Step 1.5.2

Subtract $12 h$ from $10 h$ .

$9 h^{2} - 8 h^{2} - 2 h + 15$

Step 2

Subtract $8 h^{2}$ from $9 h^{2}$ .

$h^{2} - 2 h + 15$