Pre-Algebra Examples

$(7 w - 14) (w^{2} - 9 w + 14) = 0$

Step 1

Simplify $(7 w - 14) (w^{2} - 9 w + 14)$ .

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Step 1.1

Expand $(7 w - 14) (w^{2} - 9 w + 14)$ by multiplying each term in the first expression by each term in the second expression.

$7 w \cdot w^{2} + 7 w (- 9 w) + 7 w \cdot 14 - 14 w^{2} - 14 (- 9 w) - 14 \cdot 14 = 0$

Step 1.2

Simplify terms.

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

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

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Step 1.2.1.1.1

Move $w^{2}$ .

$7 (w^{2} w) + 7 w (- 9 w) + 7 w \cdot 14 - 14 w^{2} - 14 (- 9 w) - 14 \cdot 14 = 0$

Step 1.2.1.1.2

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

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Step 1.2.1.1.2.1

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

$7 (w^{2} w^{1}) + 7 w (- 9 w) + 7 w \cdot 14 - 14 w^{2} - 14 (- 9 w) - 14 \cdot 14 = 0$

Step 1.2.1.1.2.2

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

$7 w^{2 + 1} + 7 w (- 9 w) + 7 w \cdot 14 - 14 w^{2} - 14 (- 9 w) - 14 \cdot 14 = 0$

Step 1.2.1.1.3

Add $2$ and $1$ .

$7 w^{3} + 7 w (- 9 w) + 7 w \cdot 14 - 14 w^{2} - 14 (- 9 w) - 14 \cdot 14 = 0$

Step 1.2.1.2

Rewrite using the commutative property of multiplication.

$7 w^{3} + 7 \cdot - 9 w \cdot w + 7 w \cdot 14 - 14 w^{2} - 14 (- 9 w) - 14 \cdot 14 = 0$

Step 1.2.1.3

Multiply $w$ by $w$ by adding the exponents.

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Step 1.2.1.3.1

Move $w$ .

$7 w^{3} + 7 \cdot - 9 (w \cdot w) + 7 w \cdot 14 - 14 w^{2} - 14 (- 9 w) - 14 \cdot 14 = 0$

Step 1.2.1.3.2

Multiply $w$ by $w$ .

$7 w^{3} + 7 \cdot - 9 w^{2} + 7 w \cdot 14 - 14 w^{2} - 14 (- 9 w) - 14 \cdot 14 = 0$

Step 1.2.1.4

Multiply $7$ by $- 9$ .

$7 w^{3} - 63 w^{2} + 7 w \cdot 14 - 14 w^{2} - 14 (- 9 w) - 14 \cdot 14 = 0$

Step 1.2.1.5

Multiply $14$ by $7$ .

$7 w^{3} - 63 w^{2} + 98 w - 14 w^{2} - 14 (- 9 w) - 14 \cdot 14 = 0$

Step 1.2.1.6

Multiply $- 9$ by $- 14$ .

$7 w^{3} - 63 w^{2} + 98 w - 14 w^{2} + 126 w - 14 \cdot 14 = 0$

Step 1.2.1.7

Multiply $- 14$ by $14$ .

$7 w^{3} - 63 w^{2} + 98 w - 14 w^{2} + 126 w - 196 = 0$

Step 1.2.2

Simplify by adding terms.

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Step 1.2.2.1

Subtract $14 w^{2}$ from $- 63 w^{2}$ .

$7 w^{3} - 77 w^{2} + 98 w + 126 w - 196 = 0$

Step 1.2.2.2

Add $98 w$ and $126 w$ .

$7 w^{3} - 77 w^{2} + 224 w - 196 = 0$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$w = 2, 7$

Step 3