Algebra Examples

${(3 x + 3)}^{2} = 9 x^{2} + B x + 9$

Step 1

Rewrite the equation as $9 x^{2} + B x + 9 = {(3 x + 3)}^{2}$ .

$9 x^{2} + B x + 9 = {(3 x + 3)}^{2}$

Step 2

Simplify ${(3 x + 3)}^{2}$ .

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Step 2.1

Rewrite.

$9 x^{2} + B x + 9 = 0 + 0 + {(3 x + 3)}^{2}$

Step 2.2

Rewrite ${(3 x + 3)}^{2}$ as $(3 x + 3) (3 x + 3)$ .

$9 x^{2} + B x + 9 = (3 x + 3) (3 x + 3)$

Step 2.3

Expand $(3 x + 3) (3 x + 3)$ using the FOIL Method.

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Step 2.3.1

Apply the distributive property.

$9 x^{2} + B x + 9 = 3 x (3 x + 3) + 3 (3 x + 3)$

Step 2.3.2

Apply the distributive property.

$9 x^{2} + B x + 9 = 3 x (3 x) + 3 x \cdot 3 + 3 (3 x + 3)$

Step 2.3.3

Apply the distributive property.

$9 x^{2} + B x + 9 = 3 x (3 x) + 3 x \cdot 3 + 3 (3 x) + 3 \cdot 3$

Step 2.4

Simplify and combine like terms.

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Step 2.4.1

Simplify each term.

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Step 2.4.1.1

Rewrite using the commutative property of multiplication.

$9 x^{2} + B x + 9 = 3 \cdot 3 x \cdot x + 3 x \cdot 3 + 3 (3 x) + 3 \cdot 3$

Step 2.4.1.2

Multiply $x$ by $x$ by adding the exponents.

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Step 2.4.1.2.1

Move $x$ .

$9 x^{2} + B x + 9 = 3 \cdot 3 (x \cdot x) + 3 x \cdot 3 + 3 (3 x) + 3 \cdot 3$

Step 2.4.1.2.2

Multiply $x$ by $x$ .

$9 x^{2} + B x + 9 = 3 \cdot 3 x^{2} + 3 x \cdot 3 + 3 (3 x) + 3 \cdot 3$

Step 2.4.1.3

Multiply $3$ by $3$ .

$9 x^{2} + B x + 9 = 9 x^{2} + 3 x \cdot 3 + 3 (3 x) + 3 \cdot 3$

Step 2.4.1.4

Multiply $3$ by $3$ .

$9 x^{2} + B x + 9 = 9 x^{2} + 9 x + 3 (3 x) + 3 \cdot 3$

Step 2.4.1.5

Multiply $3$ by $3$ .

$9 x^{2} + B x + 9 = 9 x^{2} + 9 x + 9 x + 3 \cdot 3$

Step 2.4.1.6

Multiply $3$ by $3$ .

$9 x^{2} + B x + 9 = 9 x^{2} + 9 x + 9 x + 9$

Step 2.4.2

Add $9 x$ and $9 x$ .

$9 x^{2} + B x + 9 = 9 x^{2} + 18 x + 9$

Step 3

Move all terms not containing $B$ to the right side of the equation.

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Step 3.1

Subtract $9 x^{2}$ from both sides of the equation.

$B x + 9 = 9 x^{2} + 18 x + 9 - 9 x^{2}$

Step 3.2

Subtract $9$ from both sides of the equation.

$B x = 9 x^{2} + 18 x + 9 - 9 x^{2} - 9$

Step 3.3

Combine the opposite terms in $9 x^{2} + 18 x + 9 - 9 x^{2} - 9$ .

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Step 3.3.1

Subtract $9 x^{2}$ from $9 x^{2}$ .

$B x = 18 x + 9 + 0 - 9$

Step 3.3.2

Add $18 x + 9$ and $0$ .

$B x = 18 x + 9 - 9$

Step 3.3.3

Subtract $9$ from $9$ .

$B x = 18 x + 0$

Step 3.3.4

Add $18 x$ and $0$ .

$B x = 18 x$

Step 4

Divide each term in $B x = 18 x$ by $x$ and simplify.

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Step 4.1

Divide each term in $B x = 18 x$ by $x$ .

$\frac{B x}{x} = \frac{18 x}{x}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $x$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{B x}{x} = \frac{18 x}{x}$

Step 4.2.1.2

Divide $B$ by $1$ .

$B = \frac{18 x}{x}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Cancel the common factor of $x$ .

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Step 4.3.1.1

Cancel the common factor.

$B = \frac{18 x}{x}$

Step 4.3.1.2

Divide $18$ by $1$ .

$B = 18$