Algebra Examples

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

Step 1

Expand $(7 x^{2} + x + 3) (x - 1)$ by multiplying each term in the first expression by each term in the second expression.

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

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

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

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Step 2.1.1.1

Move $x$ .

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

Step 2.1.1.2

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

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Step 2.1.1.2.1

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

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

Step 2.1.1.2.2

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

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

Step 2.1.1.3

Add $1$ and $2$ .

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

Step 2.1.2

Multiply $- 1$ by $7$ .

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

Step 2.1.3

Multiply $x$ by $x$ .

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

Step 2.1.4

Move $- 1$ to the left of $x$ .

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

Step 2.1.5

Rewrite $- 1 x$ as $- x$ .

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

Step 2.1.6

Multiply $3$ by $- 1$ .

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

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Add $- 7 x^{2}$ and $x^{2}$ .

$7 x^{3} - 6 x^{2} - x + 3 x - 3$

Step 2.2.2

Add $- x$ and $3 x$ .

$7 x^{3} - 6 x^{2} + 2 x - 3$