Basic Math Examples

$2 y^{2} + 13 y + 10 = {(y + 4)}^{2}$

Step 1

Simplify ${(y + 4)}^{2}$ .

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Step 1.1

Rewrite.

$2 y^{2} + 13 y + 10 = 0 + 0 + {(y + 4)}^{2}$

Step 1.2

Rewrite ${(y + 4)}^{2}$ as $(y + 4) (y + 4)$ .

$2 y^{2} + 13 y + 10 = (y + 4) (y + 4)$

Step 1.3

Expand $(y + 4) (y + 4)$ using the FOIL Method.

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Step 1.3.1

Apply the distributive property.

$2 y^{2} + 13 y + 10 = y (y + 4) + 4 (y + 4)$

Step 1.3.2

Apply the distributive property.

$2 y^{2} + 13 y + 10 = y \cdot y + y \cdot 4 + 4 (y + 4)$

Step 1.3.3

Apply the distributive property.

$2 y^{2} + 13 y + 10 = y \cdot y + y \cdot 4 + 4 y + 4 \cdot 4$

Step 1.4

Simplify and combine like terms.

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Step 1.4.1

Simplify each term.

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Step 1.4.1.1

Multiply $y$ by $y$ .

$2 y^{2} + 13 y + 10 = y^{2} + y \cdot 4 + 4 y + 4 \cdot 4$

Step 1.4.1.2

Move $4$ to the left of $y$ .

$2 y^{2} + 13 y + 10 = y^{2} + 4 \cdot y + 4 y + 4 \cdot 4$

Step 1.4.1.3

Multiply $4$ by $4$ .

$2 y^{2} + 13 y + 10 = y^{2} + 4 y + 4 y + 16$

Step 1.4.2

Add $4 y$ and $4 y$ .

$2 y^{2} + 13 y + 10 = y^{2} + 8 y + 16$

Step 2

Move all terms containing $y$ to the left side of the equation.

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Step 2.1

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

$2 y^{2} + 13 y + 10 - y^{2} = 8 y + 16$

Step 2.2

Subtract $8 y$ from both sides of the equation.

$2 y^{2} + 13 y + 10 - y^{2} - 8 y = 16$

Step 2.3

Subtract $y^{2}$ from $2 y^{2}$ .

$y^{2} + 13 y + 10 - 8 y = 16$

Step 2.4

Subtract $8 y$ from $13 y$ .

$y^{2} + 5 y + 10 = 16$

Step 3

Subtract $16$ from both sides of the equation.

$y^{2} + 5 y + 10 - 16 = 0$

Step 4

Subtract $16$ from $10$ .

$y^{2} + 5 y - 6 = 0$

Step 5

Factor $y^{2} + 5 y - 6$ using the AC method.

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Step 5.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 6$ and whose sum is $5$ .

$- 1, 6$

Step 5.2

Write the factored form using these integers.

$(y - 1) (y + 6) = 0$

Step 6

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$y - 1 = 0$

$y + 6 = 0$

Step 7

Set $y - 1$ equal to $0$ and solve for $y$ .

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Step 7.1

Set $y - 1$ equal to $0$ .

$y - 1 = 0$

Step 7.2

Add $1$ to both sides of the equation.

$y = 1$

Step 8

Set $y + 6$ equal to $0$ and solve for $y$ .

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Step 8.1

Set $y + 6$ equal to $0$ .

$y + 6 = 0$

Step 8.2

Subtract $6$ from both sides of the equation.

$y = - 6$

Step 9

The final solution is all the values that make $(y - 1) (y + 6) = 0$ true.

$y = 1, - 6$