Algebra Examples

$(4 x^{2} + 7 x) (5 x^{2} - 3 x)$

Step 1

Expand $(4 x^{2} + 7 x) (5 x^{2} - 3 x)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$4 x^{2} (5 x^{2} - 3 x) + 7 x (5 x^{2} - 3 x)$

Step 1.2

Apply the distributive property.

$4 x^{2} (5 x^{2}) + 4 x^{2} (- 3 x) + 7 x (5 x^{2} - 3 x)$

Step 1.3

Apply the distributive property.

$4 x^{2} (5 x^{2}) + 4 x^{2} (- 3 x) + 7 x (5 x^{2}) + 7 x (- 3 x)$

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.

$4 \cdot 5 x^{2} x^{2} + 4 x^{2} (- 3 x) + 7 x (5 x^{2}) + 7 x (- 3 x)$

Step 2.1.2

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

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Step 2.1.2.1

Move $x^{2}$ .

$4 \cdot 5 (x^{2} x^{2}) + 4 x^{2} (- 3 x) + 7 x (5 x^{2}) + 7 x (- 3 x)$

Step 2.1.2.2

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

$4 \cdot 5 x^{2 + 2} + 4 x^{2} (- 3 x) + 7 x (5 x^{2}) + 7 x (- 3 x)$

Step 2.1.2.3

Add $2$ and $2$ .

$4 \cdot 5 x^{4} + 4 x^{2} (- 3 x) + 7 x (5 x^{2}) + 7 x (- 3 x)$

Step 2.1.3

Multiply $4$ by $5$ .

$20 x^{4} + 4 x^{2} (- 3 x) + 7 x (5 x^{2}) + 7 x (- 3 x)$

Step 2.1.4

Rewrite using the commutative property of multiplication.

$20 x^{4} + 4 \cdot - 3 x^{2} x + 7 x (5 x^{2}) + 7 x (- 3 x)$

Step 2.1.5

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

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Step 2.1.5.1

Move $x$ .

$20 x^{4} + 4 \cdot - 3 (x \cdot x^{2}) + 7 x (5 x^{2}) + 7 x (- 3 x)$

Step 2.1.5.2

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

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Step 2.1.5.2.1

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

$20 x^{4} + 4 \cdot - 3 (x^{1} x^{2}) + 7 x (5 x^{2}) + 7 x (- 3 x)$

Step 2.1.5.2.2

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

$20 x^{4} + 4 \cdot - 3 x^{1 + 2} + 7 x (5 x^{2}) + 7 x (- 3 x)$

Step 2.1.5.3

Add $1$ and $2$ .

$20 x^{4} + 4 \cdot - 3 x^{3} + 7 x (5 x^{2}) + 7 x (- 3 x)$

Step 2.1.6

Multiply $4$ by $- 3$ .

$20 x^{4} - 12 x^{3} + 7 x (5 x^{2}) + 7 x (- 3 x)$

Step 2.1.7

Rewrite using the commutative property of multiplication.

$20 x^{4} - 12 x^{3} + 7 \cdot 5 x \cdot x^{2} + 7 x (- 3 x)$

Step 2.1.8

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

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Step 2.1.8.1

Move $x^{2}$ .

$20 x^{4} - 12 x^{3} + 7 \cdot 5 (x^{2} x) + 7 x (- 3 x)$

Step 2.1.8.2

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

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Step 2.1.8.2.1

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

$20 x^{4} - 12 x^{3} + 7 \cdot 5 (x^{2} x^{1}) + 7 x (- 3 x)$

Step 2.1.8.2.2

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

$20 x^{4} - 12 x^{3} + 7 \cdot 5 x^{2 + 1} + 7 x (- 3 x)$

Step 2.1.8.3

Add $2$ and $1$ .

$20 x^{4} - 12 x^{3} + 7 \cdot 5 x^{3} + 7 x (- 3 x)$

Step 2.1.9

Multiply $7$ by $5$ .

$20 x^{4} - 12 x^{3} + 35 x^{3} + 7 x (- 3 x)$

Step 2.1.10

Rewrite using the commutative property of multiplication.

$20 x^{4} - 12 x^{3} + 35 x^{3} + 7 \cdot - 3 x \cdot x$

Step 2.1.11

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

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Step 2.1.11.1

Move $x$ .

$20 x^{4} - 12 x^{3} + 35 x^{3} + 7 \cdot - 3 (x \cdot x)$

Step 2.1.11.2

Multiply $x$ by $x$ .

$20 x^{4} - 12 x^{3} + 35 x^{3} + 7 \cdot - 3 x^{2}$

Step 2.1.12

Multiply $7$ by $- 3$ .

$20 x^{4} - 12 x^{3} + 35 x^{3} - 21 x^{2}$

Step 2.2

Add $- 12 x^{3}$ and $35 x^{3}$ .

$20 x^{4} + 23 x^{3} - 21 x^{2}$