Basic Math Examples

$(1 - h) (1 - h) (2 - h) - (1 - h)$

Step 1

Simplify each term.

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Step 1.1

Expand $(1 - h) (1 - h)$ using the FOIL Method.

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Step 1.1.1

Apply the distributive property.

$(1 (1 - h) - h (1 - h)) (2 - h) - (1 - h)$

Step 1.1.2

Apply the distributive property.

$(1 \cdot 1 + 1 (- h) - h (1 - h)) (2 - h) - (1 - h)$

Step 1.1.3

Apply the distributive property.

$(1 \cdot 1 + 1 (- h) - h \cdot 1 - h (- h)) (2 - h) - (1 - h)$

Step 1.2

Simplify and combine like terms.

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

Multiply $1$ by $1$ .

$(1 + 1 (- h) - h \cdot 1 - h (- h)) (2 - h) - (1 - h)$

Step 1.2.1.2

Multiply $- h$ by $1$ .

$(1 - h - h \cdot 1 - h (- h)) (2 - h) - (1 - h)$

Step 1.2.1.3

Multiply $- 1$ by $1$ .

$(1 - h - h - h (- h)) (2 - h) - (1 - h)$

Step 1.2.1.4

Rewrite using the commutative property of multiplication.

$(1 - h - h - 1 \cdot - 1 h \cdot h) (2 - h) - (1 - h)$

Step 1.2.1.5

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

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Step 1.2.1.5.1

Move $h$ .

$(1 - h - h - 1 \cdot - 1 (h \cdot h)) (2 - h) - (1 - h)$

Step 1.2.1.5.2

Multiply $h$ by $h$ .

$(1 - h - h - 1 \cdot - 1 h^{2}) (2 - h) - (1 - h)$

Step 1.2.1.6

Multiply $- 1$ by $- 1$ .

$(1 - h - h + 1 h^{2}) (2 - h) - (1 - h)$

Step 1.2.1.7

Multiply $h^{2}$ by $1$ .

$(1 - h - h + h^{2}) (2 - h) - (1 - h)$

Step 1.2.2

Subtract $h$ from $- h$ .

$(1 - 2 h + h^{2}) (2 - h) - (1 - h)$

Step 1.3

Expand $(1 - 2 h + h^{2}) (2 - h)$ by multiplying each term in the first expression by each term in the second expression.

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

Step 1.4

Simplify each term.

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Step 1.4.1

Multiply $2$ by $1$ .

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

Step 1.4.2

Multiply $- h$ by $1$ .

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

Step 1.4.3

Multiply $2$ by $- 2$ .

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

Step 1.4.4

Rewrite using the commutative property of multiplication.

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

Step 1.4.5

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

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Step 1.4.5.1

Move $h$ .

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

Step 1.4.5.2

Multiply $h$ by $h$ .

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

Step 1.4.6

Multiply $- 2$ by $- 1$ .

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

Step 1.4.7

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

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

Step 1.4.8

Rewrite using the commutative property of multiplication.

$2 - h - 4 h + 2 h^{2} + 2 h^{2} - h^{2} h - (1 - h)$

Step 1.4.9

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

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Step 1.4.9.1

Move $h$ .

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

Step 1.4.9.2

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

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Step 1.4.9.2.1

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

$2 - h - 4 h + 2 h^{2} + 2 h^{2} - (h^{1} h^{2}) - (1 - h)$

Step 1.4.9.2.2

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

$2 - h - 4 h + 2 h^{2} + 2 h^{2} - h^{1 + 2} - (1 - h)$

Step 1.4.9.3

Add $1$ and $2$ .

$2 - h - 4 h + 2 h^{2} + 2 h^{2} - h^{3} - (1 - h)$

Step 1.5

Subtract $4 h$ from $- h$ .

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

Step 1.6

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

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

Step 1.7

Apply the distributive property.

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

Step 1.8

Multiply $- 1$ by $1$ .

$2 - 5 h + 4 h^{2} - h^{3} - 1 - - h$

Step 1.9

Multiply $- - h$ .

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Step 1.9.1

Multiply $- 1$ by $- 1$ .

$2 - 5 h + 4 h^{2} - h^{3} - 1 + 1 h$

Step 1.9.2

Multiply $h$ by $1$ .

$2 - 5 h + 4 h^{2} - h^{3} - 1 + h$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $1$ from $2$ .

$- 5 h + 4 h^{2} - h^{3} + 1 + h$

Step 2.2

Add $- 5 h$ and $h$ .

$4 h^{2} - h^{3} + 1 - 4 h$

Step 2.3

Simplify the expression.

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Step 2.3.1

Move $1$ .

$4 h^{2} - h^{3} - 4 h + 1$

Step 2.3.2

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

$- h^{3} + 4 h^{2} - 4 h + 1$