Algebra Examples

$10 (x - 2) - 5 (x^{2} - 7 x) + x (3 x + 6)$

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.

$10 x + 10 \cdot - 2 - 5 (x^{2} - 7 x) + x (3 x + 6)$

Step 2.2

Multiply $10$ by $- 2$ .

$10 x - 20 - 5 (x^{2} - 7 x) + x (3 x + 6)$

Step 2.3

Apply the distributive property.

$10 x - 20 - 5 x^{2} - 5 (- 7 x) + x (3 x + 6)$

Step 2.4

Multiply $- 7$ by $- 5$ .

$10 x - 20 - 5 x^{2} + 35 x + x (3 x + 6)$

Step 2.5

Apply the distributive property.

$10 x - 20 - 5 x^{2} + 35 x + x (3 x) + x \cdot 6$

Step 2.6

Rewrite using the commutative property of multiplication.

$10 x - 20 - 5 x^{2} + 35 x + 3 x \cdot x + x \cdot 6$

Step 2.7

Move $6$ to the left of $x$ .

$10 x - 20 - 5 x^{2} + 35 x + 3 x \cdot x + 6 \cdot x$

Step 2.8

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

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Step 2.8.1

Move $x$ .

$10 x - 20 - 5 x^{2} + 35 x + 3 (x \cdot x) + 6 \cdot x$

Step 2.8.2

Multiply $x$ by $x$ .

$10 x - 20 - 5 x^{2} + 35 x + 3 x^{2} + 6 \cdot x$

$10 x - 20 - 5 x^{2} + 35 x + 3 x^{2} + 6 x$

Step 3

Simplify by adding terms.

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Step 3.1

Add $10 x$ and $35 x$ .

$45 x - 20 - 5 x^{2} + 3 x^{2} + 6 x$

Step 3.2

Add $45 x$ and $6 x$ .

$- 20 - 5 x^{2} + 3 x^{2} + 51 x$

Step 3.3

Add $- 5 x^{2}$ and $3 x^{2}$ .

$- 20 - 2 x^{2} + 51 x$

Step 3.4

Move $- 20$ .

$- 2 x^{2} + 51 x - 20$