Solve 1/2(4x-5)(2x+6)

$$\frac { 1 } { 2 } ( 4 x - 5 ) ( 2 x + 6 )$$

Evaluate

$$\left(4x-5\right)\left(x+3\right)$$

Solution Steps

Use the distributive property to multiply \frac{1}{2} by 4x-5.

$$\left(\frac{1}{2}\times 4x+\frac{1}{2}\left(-5\right)\right)\left(2x+6\right)$$

Multiply \frac{1}{2} and 4 to get \frac{4}{2}.

$$\left(\frac{4}{2}x+\frac{1}{2}\left(-5\right)\right)\left(2x+6\right)$$

Divide 4 by 2 to get 2.

$$\left(2x+\frac{1}{2}\left(-5\right)\right)\left(2x+6\right)$$

Multiply \frac{1}{2} and -5 to get \frac{-5}{2}.

$$\left(2x+\frac{-5}{2}\right)\left(2x+6\right)$$

Fraction \frac{-5}{2} can be rewritten as -\frac{5}{2} by extracting the negative sign.

$$\left(2x-\frac{5}{2}\right)\left(2x+6\right)$$

Apply the distributive property by multiplying each term of 2x-\frac{5}{2} by each term of 2x+6.

$$4x^{2}+12x-\frac{5}{2}\times 2x-\frac{5}{2}\times 6$$

Cancel out 2 and 2.

$$4x^{2}+12x-5x-\frac{5}{2}\times 6$$

Combine 12x and -5x to get 7x.

$$4x^{2}+7x-\frac{5}{2}\times 6$$

Express -\frac{5}{2}\times 6 as a single fraction.

$$4x^{2}+7x+\frac{-5\times 6}{2}$$

Multiply -5 and 6 to get -30.

$$4x^{2}+7x+\frac{-30}{2}$$

Divide -30 by 2 to get -15.

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

Expand

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

Solution Steps

Use the distributive property to multiply \frac{1}{2} by 4x-5.

$$\left(\frac{1}{2}\times 4x+\frac{1}{2}\left(-5\right)\right)\left(2x+6\right)$$

Multiply \frac{1}{2} and 4 to get \frac{4}{2}.

$$\left(\frac{4}{2}x+\frac{1}{2}\left(-5\right)\right)\left(2x+6\right)$$

Divide 4 by 2 to get 2.

$$\left(2x+\frac{1}{2}\left(-5\right)\right)\left(2x+6\right)$$

Multiply \frac{1}{2} and -5 to get \frac{-5}{2}.

$$\left(2x+\frac{-5}{2}\right)\left(2x+6\right)$$

Fraction \frac{-5}{2} can be rewritten as -\frac{5}{2} by extracting the negative sign.

$$\left(2x-\frac{5}{2}\right)\left(2x+6\right)$$

Apply the distributive property by multiplying each term of 2x-\frac{5}{2} by each term of 2x+6.

$$4x^{2}+12x-\frac{5}{2}\times 2x-\frac{5}{2}\times 6$$

Cancel out 2 and 2.

$$4x^{2}+12x-5x-\frac{5}{2}\times 6$$

Combine 12x and -5x to get 7x.

$$4x^{2}+7x-\frac{5}{2}\times 6$$

Express -\frac{5}{2}\times 6 as a single fraction.

$$4x^{2}+7x+\frac{-5\times 6}{2}$$

Multiply -5 and 6 to get -30.

$$4x^{2}+7x+\frac{-30}{2}$$

Divide -30 by 2 to get -15.

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