Algebra Examples

$x^{3} + x^{2} + 1$ , $x^{2} + 7 x + 1$

Subtract the second expression $x^{2} + 7 x + 1$ from the first expression $x^{3} + x^{2} + 1$ .

$x^{3} + x^{2} + 1 - (x^{2} + 7 x + 1)$

Simplify each term.

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Apply the distributive property.

$x^{3} + x^{2} + 1 + (- x^{2} - (7 x) - 1 \cdot 1)$

Simplify.

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Multiply $7$ by $- 1$ to get $- 7$ .

$x^{3} + x^{2} + 1 + (- x^{2} - 7 x - 1 \cdot 1)$

Multiply $- 1$ by $1$ to get $- 1$ .

$x^{3} + x^{2} + 1 + (- x^{2} - 7 x - 1)$

Simplify by adding terms.

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Remove unnecessary parentheses.

$x^{3} + x^{2} + 1 - x^{2} - 7 x - 1$

Subtract $x^{2}$ from $x^{2}$ to get $0$ .

$x^{3} + 0 + 1 - 7 x - 1$

Simplify by subtracting numbers.

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Add $x^{3}$ and $0$ to get $x^{3}$ .

$x^{3} + 1 - 7 x - 1$

Subtract $1$ from $1$ to get $0$ .

$x^{3} - 7 x + 0$

Add $x^{3}$ and $0$ to get $x^{3}$ .

$x^{3} - 7 x$

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