Algebra Examples

$y = {(2 x + 5)}^{2}$

Step 1

Simplify ${(2 x + 5)}^{2}$ .

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Step 1.1

Rewrite ${(2 x + 5)}^{2}$ as $(2 x + 5) (2 x + 5)$ .

$y = (2 x + 5) (2 x + 5)$

Step 1.2

Expand $(2 x + 5) (2 x + 5)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$y = 2 x (2 x + 5) + 5 (2 x + 5)$

Step 1.2.2

Apply the distributive property.

$y = 2 x (2 x) + 2 x \cdot 5 + 5 (2 x + 5)$

Step 1.2.3

Apply the distributive property.

$y = 2 x (2 x) + 2 x \cdot 5 + 5 (2 x) + 5 \cdot 5$

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.

$y = 2 \cdot 2 x \cdot x + 2 x \cdot 5 + 5 (2 x) + 5 \cdot 5$

Step 1.3.1.2

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

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Step 1.3.1.2.1

Move $x$ .

$y = 2 \cdot 2 (x \cdot x) + 2 x \cdot 5 + 5 (2 x) + 5 \cdot 5$

Step 1.3.1.2.2

Multiply $x$ by $x$ .

$y = 2 \cdot 2 x^{2} + 2 x \cdot 5 + 5 (2 x) + 5 \cdot 5$

Step 1.3.1.3

Multiply $2$ by $2$ .

$y = 4 x^{2} + 2 x \cdot 5 + 5 (2 x) + 5 \cdot 5$

Step 1.3.1.4

Multiply $5$ by $2$ .

$y = 4 x^{2} + 10 x + 5 (2 x) + 5 \cdot 5$

Step 1.3.1.5

Multiply $2$ by $5$ .

$y = 4 x^{2} + 10 x + 10 x + 5 \cdot 5$

Step 1.3.1.6

Multiply $5$ by $5$ .

$y = 4 x^{2} + 10 x + 10 x + 25$

Step 1.3.2

Add $10 x$ and $10 x$ .

$y = 4 x^{2} + 20 x + 25$

Step 2

A linear equation is an equation of a straight line, which means that the degree of a linear equation must be $0$ or $1$ for each of its variables. In this case, the degree of variable $y$ is $1$ and the degree of variable $x$ is $2$ .

Not Linear