Algebra Examples

$(2 x^{2} + 3) (4 x + 5) - 8 x (x^{2} - 2)$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Apply the distributive property.

$2 x^{2} (4 x + 5) + 3 (4 x + 5) - 8 x (x^{2} - 2)$

Step 1.1.2

Apply the distributive property.

$2 x^{2} (4 x) + 2 x^{2} \cdot 5 + 3 (4 x + 5) - 8 x (x^{2} - 2)$

Step 1.1.3

Apply the distributive property.

$2 x^{2} (4 x) + 2 x^{2} \cdot 5 + 3 (4 x) + 3 \cdot 5 - 8 x (x^{2} - 2)$

Step 1.2

Simplify each term.

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Step 1.2.1

Rewrite using the commutative property of multiplication.

$2 \cdot 4 x^{2} x + 2 x^{2} \cdot 5 + 3 (4 x) + 3 \cdot 5 - 8 x (x^{2} - 2)$

Step 1.2.2

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

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Step 1.2.2.1

Move $x$ .

$2 \cdot 4 (x \cdot x^{2}) + 2 x^{2} \cdot 5 + 3 (4 x) + 3 \cdot 5 - 8 x (x^{2} - 2)$

Step 1.2.2.2

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

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Step 1.2.2.2.1

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

$2 \cdot 4 (x^{1} x^{2}) + 2 x^{2} \cdot 5 + 3 (4 x) + 3 \cdot 5 - 8 x (x^{2} - 2)$

Step 1.2.2.2.2

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

$2 \cdot 4 x^{1 + 2} + 2 x^{2} \cdot 5 + 3 (4 x) + 3 \cdot 5 - 8 x (x^{2} - 2)$

Step 1.2.2.3

Add $1$ and $2$ .

$2 \cdot 4 x^{3} + 2 x^{2} \cdot 5 + 3 (4 x) + 3 \cdot 5 - 8 x (x^{2} - 2)$

Step 1.2.3

Multiply $2$ by $4$ .

$8 x^{3} + 2 x^{2} \cdot 5 + 3 (4 x) + 3 \cdot 5 - 8 x (x^{2} - 2)$

Step 1.2.4

Multiply $5$ by $2$ .

$8 x^{3} + 10 x^{2} + 3 (4 x) + 3 \cdot 5 - 8 x (x^{2} - 2)$

Step 1.2.5

Multiply $4$ by $3$ .

$8 x^{3} + 10 x^{2} + 12 x + 3 \cdot 5 - 8 x (x^{2} - 2)$

Step 1.2.6

Multiply $3$ by $5$ .

$8 x^{3} + 10 x^{2} + 12 x + 15 - 8 x (x^{2} - 2)$

Step 1.3

Apply the distributive property.

$8 x^{3} + 10 x^{2} + 12 x + 15 - 8 x \cdot x^{2} - 8 x \cdot - 2$

Step 1.4

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

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Step 1.4.1

Move $x^{2}$ .

$8 x^{3} + 10 x^{2} + 12 x + 15 - 8 (x^{2} x) - 8 x \cdot - 2$

Step 1.4.2

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

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Step 1.4.2.1

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

$8 x^{3} + 10 x^{2} + 12 x + 15 - 8 (x^{2} x^{1}) - 8 x \cdot - 2$

Step 1.4.2.2

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

$8 x^{3} + 10 x^{2} + 12 x + 15 - 8 x^{2 + 1} - 8 x \cdot - 2$

Step 1.4.3

Add $2$ and $1$ .

$8 x^{3} + 10 x^{2} + 12 x + 15 - 8 x^{3} - 8 x \cdot - 2$

Step 1.5

Multiply $- 2$ by $- 8$ .

$8 x^{3} + 10 x^{2} + 12 x + 15 - 8 x^{3} + 16 x$

Step 2

Simplify by adding terms.

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Step 2.1

Combine the opposite terms in $8 x^{3} + 10 x^{2} + 12 x + 15 - 8 x^{3} + 16 x$ .

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Step 2.1.1

Subtract $8 x^{3}$ from $8 x^{3}$ .

$10 x^{2} + 12 x + 15 + 0 + 16 x$

Step 2.1.2

Add $10 x^{2} + 12 x + 15$ and $0$ .

$10 x^{2} + 12 x + 15 + 16 x$

Step 2.2

Add $12 x$ and $16 x$ .

$10 x^{2} + 28 x + 15$