Algebra Examples

$(4 + 5 h) (16 - 20 h + 25 h^{2})$

Step 1

Expand $(4 + 5 h) (16 - 20 h + 25 h^{2})$ by multiplying each term in the first expression by each term in the second expression.

$4 \cdot 16 + 4 (- 20 h) + 4 (25 h^{2}) + 5 h \cdot 16 + 5 h (- 20 h) + 5 h (25 h^{2})$

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $4$ by $16$ .

$64 + 4 (- 20 h) + 4 (25 h^{2}) + 5 h \cdot 16 + 5 h (- 20 h) + 5 h (25 h^{2})$

Step 2.1.2

Multiply $- 20$ by $4$ .

$64 - 80 h + 4 (25 h^{2}) + 5 h \cdot 16 + 5 h (- 20 h) + 5 h (25 h^{2})$

Step 2.1.3

Multiply $25$ by $4$ .

$64 - 80 h + 100 h^{2} + 5 h \cdot 16 + 5 h (- 20 h) + 5 h (25 h^{2})$

Step 2.1.4

Multiply $16$ by $5$ .

$64 - 80 h + 100 h^{2} + 80 h + 5 h (- 20 h) + 5 h (25 h^{2})$

Step 2.1.5

Rewrite using the commutative property of multiplication.

$64 - 80 h + 100 h^{2} + 80 h + 5 \cdot - 20 h \cdot h + 5 h (25 h^{2})$

Step 2.1.6

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

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Step 2.1.6.1

Move $h$ .

$64 - 80 h + 100 h^{2} + 80 h + 5 \cdot - 20 (h \cdot h) + 5 h (25 h^{2})$

Step 2.1.6.2

Multiply $h$ by $h$ .

$64 - 80 h + 100 h^{2} + 80 h + 5 \cdot - 20 h^{2} + 5 h (25 h^{2})$

Step 2.1.7

Multiply $5$ by $- 20$ .

$64 - 80 h + 100 h^{2} + 80 h - 100 h^{2} + 5 h (25 h^{2})$

Step 2.1.8

Rewrite using the commutative property of multiplication.

$64 - 80 h + 100 h^{2} + 80 h - 100 h^{2} + 5 \cdot 25 h \cdot h^{2}$

Step 2.1.9

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

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Step 2.1.9.1

Move $h^{2}$ .

$64 - 80 h + 100 h^{2} + 80 h - 100 h^{2} + 5 \cdot 25 (h^{2} h)$

Step 2.1.9.2

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

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Step 2.1.9.2.1

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

$64 - 80 h + 100 h^{2} + 80 h - 100 h^{2} + 5 \cdot 25 (h^{2} h^{1})$

Step 2.1.9.2.2

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

$64 - 80 h + 100 h^{2} + 80 h - 100 h^{2} + 5 \cdot 25 h^{2 + 1}$

Step 2.1.9.3

Add $2$ and $1$ .

$64 - 80 h + 100 h^{2} + 80 h - 100 h^{2} + 5 \cdot 25 h^{3}$

Step 2.1.10

Multiply $5$ by $25$ .

$64 - 80 h + 100 h^{2} + 80 h - 100 h^{2} + 125 h^{3}$

Step 2.2

Combine the opposite terms in $64 - 80 h + 100 h^{2} + 80 h - 100 h^{2} + 125 h^{3}$ .

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Step 2.2.1

Add $- 80 h$ and $80 h$ .

$64 + 100 h^{2} + 0 - 100 h^{2} + 125 h^{3}$

Step 2.2.2

Add $64 + 100 h^{2}$ and $0$ .

$64 + 100 h^{2} - 100 h^{2} + 125 h^{3}$

Step 2.2.3

Subtract $100 h^{2}$ from $100 h^{2}$ .

$64 + 0 + 125 h^{3}$

Step 2.2.4

Add $64$ and $0$ .

$64 + 125 h^{3}$