Algebra Examples

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

Step 1

Expand $(3 x + 5) (3 x - 5)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Rewrite using the commutative property of multiplication.

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

Step 2.1.2

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

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Step 2.1.2.1

Move $x$ .

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

Step 2.1.2.2

Multiply $x$ by $x$ .

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

Step 2.1.3

Multiply $3$ by $3$ .

$(9 x^{2} + 3 x \cdot - 5 + 5 (3 x) + 5 \cdot - 5) (5 y + 6 x)$

Step 2.1.4

Multiply $- 5$ by $3$ .

$(9 x^{2} - 15 x + 5 (3 x) + 5 \cdot - 5) (5 y + 6 x)$

Step 2.1.5

Multiply $3$ by $5$ .

$(9 x^{2} - 15 x + 15 x + 5 \cdot - 5) (5 y + 6 x)$

Step 2.1.6

Multiply $5$ by $- 5$ .

$(9 x^{2} - 15 x + 15 x - 25) (5 y + 6 x)$

Step 2.2

Add $- 15 x$ and $15 x$ .

$(9 x^{2} + 0 - 25) (5 y + 6 x)$

Step 2.3

Add $9 x^{2}$ and $0$ .

$(9 x^{2} - 25) (5 y + 6 x)$

Step 3

Expand $(9 x^{2} - 25) (5 y + 6 x)$ using the FOIL Method.

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Step 3.1

Apply the distributive property.

$9 x^{2} (5 y + 6 x) - 25 (5 y + 6 x)$

Step 3.2

Apply the distributive property.

$9 x^{2} (5 y) + 9 x^{2} (6 x) - 25 (5 y + 6 x)$

Step 3.3

Apply the distributive property.

$9 x^{2} (5 y) + 9 x^{2} (6 x) - 25 (5 y) - 25 (6 x)$

Step 4

Simplify each term.

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Step 4.1

Rewrite using the commutative property of multiplication.

$9 \cdot 5 x^{2} y + 9 x^{2} (6 x) - 25 (5 y) - 25 (6 x)$

Step 4.2

Multiply $9$ by $5$ .

$45 x^{2} y + 9 x^{2} (6 x) - 25 (5 y) - 25 (6 x)$

Step 4.3

Rewrite using the commutative property of multiplication.

$45 x^{2} y + 9 \cdot 6 x^{2} x - 25 (5 y) - 25 (6 x)$

Step 4.4

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

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Step 4.4.1

Move $x$ .

$45 x^{2} y + 9 \cdot 6 (x \cdot x^{2}) - 25 (5 y) - 25 (6 x)$

Step 4.4.2

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

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Step 4.4.2.1

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

$45 x^{2} y + 9 \cdot 6 (x^{1} x^{2}) - 25 (5 y) - 25 (6 x)$

Step 4.4.2.2

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

$45 x^{2} y + 9 \cdot 6 x^{1 + 2} - 25 (5 y) - 25 (6 x)$

Step 4.4.3

Add $1$ and $2$ .

$45 x^{2} y + 9 \cdot 6 x^{3} - 25 (5 y) - 25 (6 x)$

Step 4.5

Multiply $9$ by $6$ .

$45 x^{2} y + 54 x^{3} - 25 (5 y) - 25 (6 x)$

Step 4.6

Multiply $5$ by $- 25$ .

$45 x^{2} y + 54 x^{3} - 125 y - 25 (6 x)$

Step 4.7

Multiply $6$ by $- 25$ .

$45 x^{2} y + 54 x^{3} - 125 y - 150 x$