Basic Math Examples

${(m^{11} - 9)}^{2} - 151$

Step 1

Simplify each term.

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Step 1.1

Rewrite ${(m^{11} - 9)}^{2}$ as $(m^{11} - 9) (m^{11} - 9)$ .

$(m^{11} - 9) (m^{11} - 9) - 151$

Step 1.2

Expand $(m^{11} - 9) (m^{11} - 9)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$m^{11} (m^{11} - 9) - 9 (m^{11} - 9) - 151$

Step 1.2.2

Apply the distributive property.

$m^{11} m^{11} + m^{11} \cdot - 9 - 9 (m^{11} - 9) - 151$

Step 1.2.3

Apply the distributive property.

$m^{11} m^{11} + m^{11} \cdot - 9 - 9 m^{11} - 9 \cdot - 9 - 151$

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Multiply $m^{11}$ by $m^{11}$ by adding the exponents.

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Step 1.3.1.1.1

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

$m^{11 + 11} + m^{11} \cdot - 9 - 9 m^{11} - 9 \cdot - 9 - 151$

Step 1.3.1.1.2

Add $11$ and $11$ .

$m^{22} + m^{11} \cdot - 9 - 9 m^{11} - 9 \cdot - 9 - 151$

Step 1.3.1.2

Move $- 9$ to the left of $m^{11}$ .

$m^{22} - 9 \cdot m^{11} - 9 m^{11} - 9 \cdot - 9 - 151$

Step 1.3.1.3

Multiply $- 9$ by $- 9$ .

$m^{22} - 9 m^{11} - 9 m^{11} + 81 - 151$

Step 1.3.2

Subtract $9 m^{11}$ from $- 9 m^{11}$ .

$m^{22} - 18 m^{11} + 81 - 151$

Step 2

Subtract $151$ from $81$ .

$m^{22} - 18 m^{11} - 70$