Algebra Examples

${(2 x + 3)}^{2} + (x + 6) (x - 5)$

Step 1

Simplify each term.

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Step 1.1

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

$(2 x + 3) (2 x + 3) + (x + 6) (x - 5)$

Step 1.2

Expand $(2 x + 3) (2 x + 3)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$2 x (2 x + 3) + 3 (2 x + 3) + (x + 6) (x - 5)$

Step 1.2.2

Apply the distributive property.

$2 x (2 x) + 2 x \cdot 3 + 3 (2 x + 3) + (x + 6) (x - 5)$

Step 1.2.3

Apply the distributive property.

$2 x (2 x) + 2 x \cdot 3 + 3 (2 x) + 3 \cdot 3 + (x + 6) (x - 5)$

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

Rewrite using the commutative property of multiplication.

$2 \cdot 2 x \cdot x + 2 x \cdot 3 + 3 (2 x) + 3 \cdot 3 + (x + 6) (x - 5)$

Step 1.3.1.2

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

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Step 1.3.1.2.1

Move $x$ .

$2 \cdot 2 (x \cdot x) + 2 x \cdot 3 + 3 (2 x) + 3 \cdot 3 + (x + 6) (x - 5)$

Step 1.3.1.2.2

Multiply $x$ by $x$ .

$2 \cdot 2 x^{2} + 2 x \cdot 3 + 3 (2 x) + 3 \cdot 3 + (x + 6) (x - 5)$

Step 1.3.1.3

Multiply $2$ by $2$ .

$4 x^{2} + 2 x \cdot 3 + 3 (2 x) + 3 \cdot 3 + (x + 6) (x - 5)$

Step 1.3.1.4

Multiply $3$ by $2$ .

$4 x^{2} + 6 x + 3 (2 x) + 3 \cdot 3 + (x + 6) (x - 5)$

Step 1.3.1.5

Multiply $2$ by $3$ .

$4 x^{2} + 6 x + 6 x + 3 \cdot 3 + (x + 6) (x - 5)$

Step 1.3.1.6

Multiply $3$ by $3$ .

$4 x^{2} + 6 x + 6 x + 9 + (x + 6) (x - 5)$

Step 1.3.2

Add $6 x$ and $6 x$ .

$4 x^{2} + 12 x + 9 + (x + 6) (x - 5)$

Step 1.4

Expand $(x + 6) (x - 5)$ using the FOIL Method.

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Step 1.4.1

Apply the distributive property.

$4 x^{2} + 12 x + 9 + x (x - 5) + 6 (x - 5)$

Step 1.4.2

Apply the distributive property.

$4 x^{2} + 12 x + 9 + x \cdot x + x \cdot - 5 + 6 (x - 5)$

Step 1.4.3

Apply the distributive property.

$4 x^{2} + 12 x + 9 + x \cdot x + x \cdot - 5 + 6 x + 6 \cdot - 5$

Step 1.5

Simplify and combine like terms.

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Step 1.5.1

Simplify each term.

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Step 1.5.1.1

Multiply $x$ by $x$ .

$4 x^{2} + 12 x + 9 + x^{2} + x \cdot - 5 + 6 x + 6 \cdot - 5$

Step 1.5.1.2

Move $- 5$ to the left of $x$ .

$4 x^{2} + 12 x + 9 + x^{2} - 5 \cdot x + 6 x + 6 \cdot - 5$

Step 1.5.1.3

Multiply $6$ by $- 5$ .

$4 x^{2} + 12 x + 9 + x^{2} - 5 x + 6 x - 30$

Step 1.5.2

Add $- 5 x$ and $6 x$ .

$4 x^{2} + 12 x + 9 + x^{2} + x - 30$

Step 2

Simplify by adding terms.

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Step 2.1

Add $4 x^{2}$ and $x^{2}$ .

$5 x^{2} + 12 x + 9 + x - 30$

Step 2.2

Add $12 x$ and $x$ .

$5 x^{2} + 13 x + 9 - 30$

Step 2.3

Subtract $30$ from $9$ .

$5 x^{2} + 13 x - 21$