Pre-Algebra Examples

$(x^{9} + x^{8}) (x^{9} + x^{8} - x^{7})$

Step 1

Expand $(x^{9} + x^{8}) (x^{9} + x^{8} - x^{7})$ by multiplying each term in the first expression by each term in the second expression.

$x^{9} x^{9} + x^{9} x^{8} + x^{9} (- x^{7}) + x^{8} x^{9} + x^{8} x^{8} + x^{8} (- x^{7})$

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $x^{9}$ by $x^{9}$ by adding the exponents.

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Step 2.1.1.1

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

$x^{9 + 9} + x^{9} x^{8} + x^{9} (- x^{7}) + x^{8} x^{9} + x^{8} x^{8} + x^{8} (- x^{7})$

Step 2.1.1.2

Add $9$ and $9$ .

$x^{18} + x^{9} x^{8} + x^{9} (- x^{7}) + x^{8} x^{9} + x^{8} x^{8} + x^{8} (- x^{7})$

Step 2.1.2

Multiply $x^{9}$ by $x^{8}$ by adding the exponents.

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Step 2.1.2.1

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

$x^{18} + x^{9 + 8} + x^{9} (- x^{7}) + x^{8} x^{9} + x^{8} x^{8} + x^{8} (- x^{7})$

Step 2.1.2.2

Add $9$ and $8$ .

$x^{18} + x^{17} + x^{9} (- x^{7}) + x^{8} x^{9} + x^{8} x^{8} + x^{8} (- x^{7})$

Step 2.1.3

Rewrite using the commutative property of multiplication.

$x^{18} + x^{17} - x^{9} x^{7} + x^{8} x^{9} + x^{8} x^{8} + x^{8} (- x^{7})$

Step 2.1.4

Multiply $x^{9}$ by $x^{7}$ by adding the exponents.

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Step 2.1.4.1

Move $x^{7}$ .

$x^{18} + x^{17} - (x^{7} x^{9}) + x^{8} x^{9} + x^{8} x^{8} + x^{8} (- x^{7})$

Step 2.1.4.2

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

$x^{18} + x^{17} - x^{7 + 9} + x^{8} x^{9} + x^{8} x^{8} + x^{8} (- x^{7})$

Step 2.1.4.3

Add $7$ and $9$ .

$x^{18} + x^{17} - x^{16} + x^{8} x^{9} + x^{8} x^{8} + x^{8} (- x^{7})$

Step 2.1.5

Multiply $x^{8}$ by $x^{9}$ by adding the exponents.

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Step 2.1.5.1

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

$x^{18} + x^{17} - x^{16} + x^{8 + 9} + x^{8} x^{8} + x^{8} (- x^{7})$

Step 2.1.5.2

Add $8$ and $9$ .

$x^{18} + x^{17} - x^{16} + x^{17} + x^{8} x^{8} + x^{8} (- x^{7})$

Step 2.1.6

Multiply $x^{8}$ by $x^{8}$ by adding the exponents.

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Step 2.1.6.1

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

$x^{18} + x^{17} - x^{16} + x^{17} + x^{8 + 8} + x^{8} (- x^{7})$

Step 2.1.6.2

Add $8$ and $8$ .

$x^{18} + x^{17} - x^{16} + x^{17} + x^{16} + x^{8} (- x^{7})$

Step 2.1.7

Rewrite using the commutative property of multiplication.

$x^{18} + x^{17} - x^{16} + x^{17} + x^{16} - x^{8} x^{7}$

Step 2.1.8

Multiply $x^{8}$ by $x^{7}$ by adding the exponents.

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Step 2.1.8.1

Move $x^{7}$ .

$x^{18} + x^{17} - x^{16} + x^{17} + x^{16} - (x^{7} x^{8})$

Step 2.1.8.2

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

$x^{18} + x^{17} - x^{16} + x^{17} + x^{16} - x^{7 + 8}$

Step 2.1.8.3

Add $7$ and $8$ .

$x^{18} + x^{17} - x^{16} + x^{17} + x^{16} - x^{15}$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Combine the opposite terms in $x^{18} + x^{17} - x^{16} + x^{17} + x^{16} - x^{15}$ .

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Step 2.2.1.1

Add $- x^{16}$ and $x^{16}$ .

$x^{18} + x^{17} + x^{17} + 0 - x^{15}$

Step 2.2.1.2

Add $x^{18} + x^{17} + x^{17}$ and $0$ .

$x^{18} + x^{17} + x^{17} - x^{15}$

Step 2.2.2

Add $x^{17}$ and $x^{17}$ .

$x^{18} + 2 x^{17} - x^{15}$