Algebra Examples

$(5 x - 3 x^{2}) - (5 x - 2) \cdot (10 x + 7 x^{2})$

Step 1

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

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

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$5 x - 3 x^{2} + (- (5 x) - - 2) \cdot (10 x + 7 x^{2})$

Step 2.2

Multiply $5$ by $- 1$ .

$5 x - 3 x^{2} + (- 5 x - - 2) \cdot (10 x + 7 x^{2})$

Step 2.3

Multiply $- 1$ by $- 2$ .

$5 x - 3 x^{2} + (- 5 x + 2) \cdot (10 x + 7 x^{2})$

Step 2.4

Expand $(- 5 x + 2) (10 x + 7 x^{2})$ using the FOIL Method.

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Step 2.4.1

Apply the distributive property.

$5 x - 3 x^{2} - 5 x (10 x + 7 x^{2}) + 2 (10 x + 7 x^{2})$

Step 2.4.2

Apply the distributive property.

$5 x - 3 x^{2} - 5 x (10 x) - 5 x (7 x^{2}) + 2 (10 x + 7 x^{2})$

Step 2.4.3

Apply the distributive property.

$5 x - 3 x^{2} - 5 x (10 x) - 5 x (7 x^{2}) + 2 (10 x) + 2 (7 x^{2})$

Step 2.5

Simplify and combine like terms.

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Step 2.5.1

Simplify each term.

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Step 2.5.1.1

Rewrite using the commutative property of multiplication.

$5 x - 3 x^{2} - 5 \cdot 10 x \cdot x - 5 x (7 x^{2}) + 2 (10 x) + 2 (7 x^{2})$

Step 2.5.1.2

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

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Step 2.5.1.2.1

Move $x$ .

$5 x - 3 x^{2} - 5 \cdot 10 (x \cdot x) - 5 x (7 x^{2}) + 2 (10 x) + 2 (7 x^{2})$

Step 2.5.1.2.2

Multiply $x$ by $x$ .

$5 x - 3 x^{2} - 5 \cdot 10 x^{2} - 5 x (7 x^{2}) + 2 (10 x) + 2 (7 x^{2})$

Step 2.5.1.3

Multiply $- 5$ by $10$ .

$5 x - 3 x^{2} - 50 x^{2} - 5 x (7 x^{2}) + 2 (10 x) + 2 (7 x^{2})$

Step 2.5.1.4

Rewrite using the commutative property of multiplication.

$5 x - 3 x^{2} - 50 x^{2} - 5 \cdot 7 x \cdot x^{2} + 2 (10 x) + 2 (7 x^{2})$

Step 2.5.1.5

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

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Step 2.5.1.5.1

Move $x^{2}$ .

$5 x - 3 x^{2} - 50 x^{2} - 5 \cdot 7 (x^{2} x) + 2 (10 x) + 2 (7 x^{2})$

Step 2.5.1.5.2

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

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Step 2.5.1.5.2.1

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

$5 x - 3 x^{2} - 50 x^{2} - 5 \cdot 7 (x^{2} x^{1}) + 2 (10 x) + 2 (7 x^{2})$

Step 2.5.1.5.2.2

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

$5 x - 3 x^{2} - 50 x^{2} - 5 \cdot 7 x^{2 + 1} + 2 (10 x) + 2 (7 x^{2})$

Step 2.5.1.5.3

Add $2$ and $1$ .

$5 x - 3 x^{2} - 50 x^{2} - 5 \cdot 7 x^{3} + 2 (10 x) + 2 (7 x^{2})$

Step 2.5.1.6

Multiply $- 5$ by $7$ .

$5 x - 3 x^{2} - 50 x^{2} - 35 x^{3} + 2 (10 x) + 2 (7 x^{2})$

Step 2.5.1.7

Multiply $10$ by $2$ .

$5 x - 3 x^{2} - 50 x^{2} - 35 x^{3} + 20 x + 2 (7 x^{2})$

Step 2.5.1.8

Multiply $7$ by $2$ .

$5 x - 3 x^{2} - 50 x^{2} - 35 x^{3} + 20 x + 14 x^{2}$

Step 2.5.2

Add $- 50 x^{2}$ and $14 x^{2}$ .

$5 x - 3 x^{2} - 36 x^{2} - 35 x^{3} + 20 x$

Step 3

Simplify by adding terms.

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Step 3.1

Add $5 x$ and $20 x$ .

$- 3 x^{2} - 36 x^{2} - 35 x^{3} + 25 x$

Step 3.2

Subtract $36 x^{2}$ from $- 3 x^{2}$ .

$- 39 x^{2} - 35 x^{3} + 25 x$

Step 3.3

Reorder $- 39 x^{2}$ and $- 35 x^{3}$ .

$- 35 x^{3} - 39 x^{2} + 25 x$