Basic Math Examples

$3 (y - 7) + 2 y = 5 {(y + 3)}^{3}$

Step 1

Simplify $3 (y - 7) + 2 y$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$3 y + 3 \cdot - 7 + 2 y = 5 {(y + 3)}^{3}$

Step 1.1.2

Multiply $3$ by $- 7$ .

$3 y - 21 + 2 y = 5 {(y + 3)}^{3}$

Step 1.2

Add $3 y$ and $2 y$ .

$5 y - 21 = 5 {(y + 3)}^{3}$

Step 2

Simplify $5 {(y + 3)}^{3}$ .

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Step 2.1

Use the Binomial Theorem.

$5 y - 21 = 5 (y^{3} + 3 y^{2} \cdot 3 + 3 y \cdot 3^{2} + 3^{3})$

Step 2.2

Simplify terms.

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Step 2.2.1

Simplify each term.

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Step 2.2.1.1

Multiply $3$ by $3$ .

$5 y - 21 = 5 (y^{3} + 9 y^{2} + 3 y \cdot 3^{2} + 3^{3})$

Step 2.2.1.2

Multiply $3$ by $3^{2}$ by adding the exponents.

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Step 2.2.1.2.1

Move $3^{2}$ .

$5 y - 21 = 5 (y^{3} + 9 y^{2} + 3^{2} \cdot 3 y + 3^{3})$

Step 2.2.1.2.2

Multiply $3^{2}$ by $3$ .

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Step 2.2.1.2.2.1

Raise $3$ to the power of $1$ .

$5 y - 21 = 5 (y^{3} + 9 y^{2} + 3^{2} \cdot 3^{1} y + 3^{3})$

Step 2.2.1.2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$5 y - 21 = 5 (y^{3} + 9 y^{2} + 3^{2 + 1} y + 3^{3})$

Step 2.2.1.2.3

Add $2$ and $1$ .

$5 y - 21 = 5 (y^{3} + 9 y^{2} + 3^{3} y + 3^{3})$

Step 2.2.1.3

Raise $3$ to the power of $3$ .

$5 y - 21 = 5 (y^{3} + 9 y^{2} + 27 y + 3^{3})$

Step 2.2.1.4

Raise $3$ to the power of $3$ .

$5 y - 21 = 5 (y^{3} + 9 y^{2} + 27 y + 27)$

Step 2.2.2

Apply the distributive property.

$5 y - 21 = 5 y^{3} + 5 (9 y^{2}) + 5 (27 y) + 5 \cdot 27$

Step 2.3

Simplify.

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Step 2.3.1

Multiply $9$ by $5$ .

$5 y - 21 = 5 y^{3} + 45 y^{2} + 5 (27 y) + 5 \cdot 27$

Step 2.3.2

Multiply $27$ by $5$ .

$5 y - 21 = 5 y^{3} + 45 y^{2} + 135 y + 5 \cdot 27$

Step 2.3.3

Multiply $5$ by $27$ .

$5 y - 21 = 5 y^{3} + 45 y^{2} + 135 y + 135$

Step 3

Graph each side of the equation. The solution is the x-value of the point of intersection.

$y \approx - 5.10318365$

Step 4