Algebra Examples

$4 x (2 x - 3) - 5 (3 x - 4)$

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.

$4 x (2 x) + 4 x \cdot - 3 - 5 (3 x - 4)$

Step 2.2

Rewrite using the commutative property of multiplication.

$4 \cdot 2 x \cdot x + 4 x \cdot - 3 - 5 (3 x - 4)$

Step 2.3

Multiply $- 3$ by $4$ .

$4 \cdot 2 x \cdot x - 12 x - 5 (3 x - 4)$

Step 2.4

Simplify each term.

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Step 2.4.1

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

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Step 2.4.1.1

Move $x$ .

$4 \cdot 2 (x \cdot x) - 12 x - 5 (3 x - 4)$

Step 2.4.1.2

Multiply $x$ by $x$ .

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

Step 2.4.2

Multiply $4$ by $2$ .

$8 x^{2} - 12 x - 5 (3 x - 4)$

Step 2.5

Apply the distributive property.

$8 x^{2} - 12 x - 5 (3 x) - 5 \cdot - 4$

Step 2.6

Multiply $3$ by $- 5$ .

$8 x^{2} - 12 x - 15 x - 5 \cdot - 4$

Step 2.7

Multiply $- 5$ by $- 4$ .

$8 x^{2} - 12 x - 15 x + 20$

Step 3

Subtract $15 x$ from $- 12 x$ .

$8 x^{2} - 27 x + 20$