Algebra Examples

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

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$y = a x^{2} + b x + c$

Step 2

Apply the distributive property.

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

Step 3

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

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Step 3.1

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

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

Step 3.2

Add $2$ and $2$ .

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

Step 4

Move $- 7$ to the left of $x^{2}$ .

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

Step 5

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

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Step 5.1

Apply the distributive property.

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

Step 5.2

Apply the distributive property.

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

Step 5.3

Apply the distributive property.

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

Step 6

Simplify each term.

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Step 6.1

Rewrite using the commutative property of multiplication.

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

Step 6.2

Multiply $x^{4}$ by $x$ by adding the exponents.

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Step 6.2.1

Move $x$ .

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

Step 6.2.2

Multiply $x$ by $x^{4}$ .

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Step 6.2.2.1

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

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

Step 6.2.2.2

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

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

Step 6.2.3

Add $1$ and $4$ .

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

Step 6.3

Move $3$ to the left of $x^{4}$ .

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

Step 6.4

Rewrite using the commutative property of multiplication.

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

Step 6.5

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

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Step 6.5.1

Move $x$ .

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

Step 6.5.2

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

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Step 6.5.2.1

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

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

Step 6.5.2.2

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

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

Step 6.5.3

Add $1$ and $2$ .

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

Step 6.6

Multiply $- 7$ by $2$ .

$y = 2 x^{5} + 3 x^{4} - 14 x^{3} - 7 x^{2} \cdot 3$

Step 6.7

Multiply $3$ by $- 7$ .

$y = 2 x^{5} + 3 x^{4} - 14 x^{3} - 21 x^{2}$

Step 7