Algebra Examples

$(h + 9) (5 h - 4 h^{2} - 10)$

Step 1

Expand $(h + 9) (5 h - 4 h^{2} - 10)$ by multiplying each term in the first expression by each term in the second expression.

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

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Rewrite using the commutative property of multiplication.

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

Step 2.1.2

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

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Step 2.1.2.1

Move $h$ .

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

Step 2.1.2.2

Multiply $h$ by $h$ .

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

Step 2.1.3

Rewrite using the commutative property of multiplication.

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

Step 2.1.4

Multiply $h$ by $h^{2}$ by adding the exponents.

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Step 2.1.4.1

Move $h^{2}$ .

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

Step 2.1.4.2

Multiply $h^{2}$ by $h$ .

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Step 2.1.4.2.1

Raise $h$ to the power of $1$ .

$5 h^{2} - 4 (h^{2} h^{1}) + h \cdot - 10 + 9 (5 h) + 9 (- 4 h^{2}) + 9 \cdot - 10$

Step 2.1.4.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$5 h^{2} - 4 h^{2 + 1} + h \cdot - 10 + 9 (5 h) + 9 (- 4 h^{2}) + 9 \cdot - 10$

Step 2.1.4.3

Add $2$ and $1$ .

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

Step 2.1.5

Move $- 10$ to the left of $h$ .

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

Step 2.1.6

Multiply $5$ by $9$ .

$5 h^{2} - 4 h^{3} - 10 h + 45 h + 9 (- 4 h^{2}) + 9 \cdot - 10$

Step 2.1.7

Multiply $- 4$ by $9$ .

$5 h^{2} - 4 h^{3} - 10 h + 45 h - 36 h^{2} + 9 \cdot - 10$

Step 2.1.8

Multiply $9$ by $- 10$ .

$5 h^{2} - 4 h^{3} - 10 h + 45 h - 36 h^{2} - 90$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Subtract $36 h^{2}$ from $5 h^{2}$ .

$- 31 h^{2} - 4 h^{3} - 10 h + 45 h - 90$

Step 2.2.2

Add $- 10 h$ and $45 h$ .

$- 31 h^{2} - 4 h^{3} + 35 h - 90$

Step 2.2.3

Reorder $- 31 h^{2}$ and $- 4 h^{3}$ .

$- 4 h^{3} - 31 h^{2} + 35 h - 90$