Basic Math Examples

${(y - 5)}^{2} + 2 {(y + 3)}^{2}$

Step 1

Simplify each term.

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Step 1.1

Rewrite ${(y - 5)}^{2}$ as $(y - 5) (y - 5)$ .

$(y - 5) (y - 5) + 2 {(y + 3)}^{2}$

Step 1.2

Expand $(y - 5) (y - 5)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$y (y - 5) - 5 (y - 5) + 2 {(y + 3)}^{2}$

Step 1.2.2

Apply the distributive property.

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

Step 1.2.3

Apply the distributive property.

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

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

Multiply $y$ by $y$ .

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

Step 1.3.1.2

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

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

Step 1.3.1.3

Multiply $- 5$ by $- 5$ .

$y^{2} - 5 y - 5 y + 25 + 2 {(y + 3)}^{2}$

Step 1.3.2

Subtract $5 y$ from $- 5 y$ .

$y^{2} - 10 y + 25 + 2 {(y + 3)}^{2}$

Step 1.4

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

$y^{2} - 10 y + 25 + 2 ((y + 3) (y + 3))$

Step 1.5

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

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Step 1.5.1

Apply the distributive property.

$y^{2} - 10 y + 25 + 2 (y (y + 3) + 3 (y + 3))$

Step 1.5.2

Apply the distributive property.

$y^{2} - 10 y + 25 + 2 (y \cdot y + y \cdot 3 + 3 (y + 3))$

Step 1.5.3

Apply the distributive property.

$y^{2} - 10 y + 25 + 2 (y \cdot y + y \cdot 3 + 3 y + 3 \cdot 3)$

Step 1.6

Simplify and combine like terms.

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Step 1.6.1

Simplify each term.

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Step 1.6.1.1

Multiply $y$ by $y$ .

$y^{2} - 10 y + 25 + 2 (y^{2} + y \cdot 3 + 3 y + 3 \cdot 3)$

Step 1.6.1.2

Move $3$ to the left of $y$ .

$y^{2} - 10 y + 25 + 2 (y^{2} + 3 \cdot y + 3 y + 3 \cdot 3)$

Step 1.6.1.3

Multiply $3$ by $3$ .

$y^{2} - 10 y + 25 + 2 (y^{2} + 3 y + 3 y + 9)$

Step 1.6.2

Add $3 y$ and $3 y$ .

$y^{2} - 10 y + 25 + 2 (y^{2} + 6 y + 9)$

Step 1.7

Apply the distributive property.

$y^{2} - 10 y + 25 + 2 y^{2} + 2 (6 y) + 2 \cdot 9$

Step 1.8

Simplify.

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Step 1.8.1

Multiply $6$ by $2$ .

$y^{2} - 10 y + 25 + 2 y^{2} + 12 y + 2 \cdot 9$

Step 1.8.2

Multiply $2$ by $9$ .

$y^{2} - 10 y + 25 + 2 y^{2} + 12 y + 18$

Step 2

Simplify by adding terms.

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Step 2.1

Add $y^{2}$ and $2 y^{2}$ .

$3 y^{2} - 10 y + 25 + 12 y + 18$

Step 2.2

Add $- 10 y$ and $12 y$ .

$3 y^{2} + 2 y + 25 + 18$

Step 2.3

Add $25$ and $18$ .

$3 y^{2} + 2 y + 43$