Basic Math Examples

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

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

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Expand

(1 - h) (1 - h)

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

Tap for more steps...

Step 1.1.1

Apply the distributive property.

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

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

Step 1.1.2

Apply the distributive property.

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

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

Step 1.1.3

Apply the distributive property.

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

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

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

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

Step 1.2

Simplify and combine like terms.

Tap for more steps...

Step 1.2.1

Simplify each term.

Tap for more steps...

Step 1.2.1.1

Multiply

1

$1$ by

1

$1$ .

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

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

Step 1.2.1.2

Multiply

- h

$- h$ by

1

$1$ .

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

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

Step 1.2.1.3

Multiply

- 1

$- 1$ by

1

$1$ .

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

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

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)

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

Step 1.2.1.5

Multiply

h

$h$ by

h

$h$ by adding the exponents.

Tap for more steps...

Step 1.2.1.5.1

Move

h

$h$ .

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

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

Step 1.2.1.5.2

Multiply

h

$h$ by

h

$h$ .

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

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

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

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

Step 1.2.1.6

Multiply

- 1

$- 1$ by

- 1

$- 1$ .

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

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

Step 1.2.1.7

Multiply

h^{2}

$h^{2}$ by

1

$1$ .

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

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

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

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

Step 1.2.2

Subtract

h

$h$ from

- h

$- h$ .

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

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

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

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

Step 1.3

Expand

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

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

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

Step 1.4

Simplify each term.

Tap for more steps...

Step 1.4.1

Multiply

2

$2$ by

1

$1$ .

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

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

Step 1.4.2

Multiply

- h

$- h$ by

1

$1$ .

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

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

Step 1.4.3

Multiply

2

$2$ by

- 2

$- 2$ .

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

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

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)

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

Step 1.4.5

Multiply

h

$h$ by

h

$h$ by adding the exponents.

Tap for more steps...

Step 1.4.5.1

Move

h

$h$ .

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

$h$ by

h

$h$ .

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

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

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

$- 2$ by

- 1

$- 1$ .

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

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

Step 1.4.7

Move

2

$2$ to the left of

h^{2}

$h^{2}$ .

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

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

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)

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

Step 1.4.9

Multiply

h^{2}

$h^{2}$ by

h

$h$ by adding the exponents.

Tap for more steps...

Step 1.4.9.1

Move

h

$h$ .

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

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

Step 1.4.9.2

Multiply

h

$h$ by

h^{2}

$h^{2}$ .

Tap for more steps...

Step 1.4.9.2.1

Raise

h

$h$ to the power of

1

$1$ .

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

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

Step 1.4.9.2.2

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

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

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

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

Step 1.4.9.3

Add

1

$1$ and

2

$2$ .

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

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

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

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

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

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

Step 1.5

Subtract

4 h

$4 h$ from

- h

$- h$ .

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

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

Step 1.6

Add

2 h^{2}

$2 h^{2}$ and

2 h^{2}

$2 h^{2}$ .

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

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

Step 1.7

Apply the distributive property.

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

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

Step 1.8

Multiply

- 1

$- 1$ by

1

$1$ .

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

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

Step 1.9

Multiply

- - h

$- - h$ .

Tap for more steps...

Step 1.9.1

Multiply

- 1

$- 1$ by

- 1

$- 1$ .

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

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

Step 1.9.2

Multiply

h

$h$ by

1

$1$ .

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

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

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

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

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

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

Step 2

Simplify by adding terms.

Tap for more steps...

Step 2.1

Subtract

1

$1$ from

2

$2$ .

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

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

Step 2.2

Add

- 5 h

$- 5 h$ and

h

$h$ .

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

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

Step 2.3

Simplify the expression.

Tap for more steps...

Step 2.3.1

Move

1

$1$ .

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

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

Step 2.3.2

Reorder

4 h^{2}

$4 h^{2}$ and

- h^{3}

$- h^{3}$ .

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

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

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

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

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

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