Basic Math Examples

$(h^{2} - 5 h + 6) (3 - h)$

Step 1

Expand $(h^{2} - 5 h + 6) (3 - h)$ by multiplying each term in the first expression by each term in the second expression.

$h^{2} \cdot 3 + h^{2} (- h) - 5 h \cdot 3 - 5 h (- h) + 6 \cdot 3 + 6 (- h)$

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Move $3$ to the left of $h^{2}$ .

$3 \cdot h^{2} + h^{2} (- h) - 5 h \cdot 3 - 5 h (- h) + 6 \cdot 3 + 6 (- h)$

Step 2.1.2

Rewrite using the commutative property of multiplication.

$3 h^{2} - h^{2} h - 5 h \cdot 3 - 5 h (- h) + 6 \cdot 3 + 6 (- h)$

Step 2.1.3

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

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Step 2.1.3.1

Move $h$ .

$3 h^{2} - (h \cdot h^{2}) - 5 h \cdot 3 - 5 h (- h) + 6 \cdot 3 + 6 (- h)$

Step 2.1.3.2

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

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Step 2.1.3.2.1

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

$3 h^{2} - (h^{1} h^{2}) - 5 h \cdot 3 - 5 h (- h) + 6 \cdot 3 + 6 (- h)$

Step 2.1.3.2.2

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

$3 h^{2} - h^{1 + 2} - 5 h \cdot 3 - 5 h (- h) + 6 \cdot 3 + 6 (- h)$

Step 2.1.3.3

Add $1$ and $2$ .

$3 h^{2} - h^{3} - 5 h \cdot 3 - 5 h (- h) + 6 \cdot 3 + 6 (- h)$

Step 2.1.4

Multiply $3$ by $- 5$ .

$3 h^{2} - h^{3} - 15 h - 5 h (- h) + 6 \cdot 3 + 6 (- h)$

Step 2.1.5

Rewrite using the commutative property of multiplication.

$3 h^{2} - h^{3} - 15 h - 5 \cdot - 1 h \cdot h + 6 \cdot 3 + 6 (- h)$

Step 2.1.6

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

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Step 2.1.6.1

Move $h$ .

$3 h^{2} - h^{3} - 15 h - 5 \cdot - 1 (h \cdot h) + 6 \cdot 3 + 6 (- h)$

Step 2.1.6.2

Multiply $h$ by $h$ .

$3 h^{2} - h^{3} - 15 h - 5 \cdot - 1 h^{2} + 6 \cdot 3 + 6 (- h)$

Step 2.1.7

Multiply $- 5$ by $- 1$ .

$3 h^{2} - h^{3} - 15 h + 5 h^{2} + 6 \cdot 3 + 6 (- h)$

Step 2.1.8

Multiply $6$ by $3$ .

$3 h^{2} - h^{3} - 15 h + 5 h^{2} + 18 + 6 (- h)$

Step 2.1.9

Multiply $- 1$ by $6$ .

$3 h^{2} - h^{3} - 15 h + 5 h^{2} + 18 - 6 h$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Add $3 h^{2}$ and $5 h^{2}$ .

$8 h^{2} - h^{3} - 15 h + 18 - 6 h$

Step 2.2.2

Subtract $6 h$ from $- 15 h$ .

$8 h^{2} - h^{3} - 21 h + 18$

Step 2.2.3

Reorder $8 h^{2}$ and $- h^{3}$ .

$- h^{3} + 8 h^{2} - 21 h + 18$