Pre-Algebra Examples

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

Step 1

Apply the distributive property.

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

Step 2

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

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Step 2.1

Move $x$ .

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

Step 2.2

Multiply $x$ by $x$ .

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

Step 3

Multiply $- 3$ by $4$ .

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

Step 4

Apply the distributive property.

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

Step 5

Multiply $- 5$ by $3$ .

$4 x^{2} - 12 x - 15 - 5 (- x)$

Step 6

Multiply $- 1$ by $- 5$ .

$4 x^{2} - 12 x - 15 + 5 x$

Step 7

Add $- 12 x$ and $5 x$ .

$4 x^{2} - 7 x - 15$

Step 8

Factor by grouping.

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Step 8.1

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 4 \cdot - 15 = - 60$ and whose sum is $b = - 7$ .

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Step 8.1.1

Factor $- 7$ out of $- 7 x$ .

$4 x^{2} - 7 (x) - 15$

Step 8.1.2

Rewrite $- 7$ as $5$ plus $- 12$

$4 x^{2} + (5 - 12) x - 15$

Step 8.1.3

Apply the distributive property.

$4 x^{2} + 5 x - 12 x - 15$

Step 8.2

Factor out the greatest common factor from each group.

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Step 8.2.1

Group the first two terms and the last two terms.

$(4 x^{2} + 5 x) - 12 x - 15$

Step 8.2.2

Factor out the greatest common factor (GCF) from each group.

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

Step 8.3

Factor the polynomial by factoring out the greatest common factor, $4 x + 5$ .

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