Solve (1/2x-5/2)(x+5)=

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

Evaluate

$$\frac{x^{2}-25}{2}$$

Solution Steps

Apply the distributive property by multiplying each term of \frac{1}{2}x-\frac{5}{2} by each term of x+5.

$$\frac{1}{2}xx+\frac{1}{2}x\times 5-\frac{5}{2}x-\frac{5}{2}\times 5$$

Multiply x and x to get x^{2}.

$$\frac{1}{2}x^{2}+\frac{1}{2}x\times 5-\frac{5}{2}x-\frac{5}{2}\times 5$$

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

$$\frac{1}{2}x^{2}+\frac{5}{2}x-\frac{5}{2}x-\frac{5}{2}\times 5$$

Combine \frac{5}{2}x and -\frac{5}{2}x to get 0.

$$\frac{1}{2}x^{2}-\frac{5}{2}\times 5$$

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

$$\frac{1}{2}x^{2}+\frac{-5\times 5}{2}$$

Multiply -5 and 5 to get -25.

$$\frac{1}{2}x^{2}+\frac{-25}{2}$$

Fraction \frac{-25}{2} can be rewritten as -\frac{25}{2} by extracting the negative sign.

$$\frac{1}{2}x^{2}-\frac{25}{2}$$

Expand

$$\frac{x^{2}-25}{2}$$

Solution Steps

Apply the distributive property by multiplying each term of \frac{1}{2}x-\frac{5}{2} by each term of x+5.

$$\frac{1}{2}xx+\frac{1}{2}x\times 5-\frac{5}{2}x-\frac{5}{2}\times 5$$

Multiply x and x to get x^{2}.

$$\frac{1}{2}x^{2}+\frac{1}{2}x\times 5-\frac{5}{2}x-\frac{5}{2}\times 5$$

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

$$\frac{1}{2}x^{2}+\frac{5}{2}x-\frac{5}{2}x-\frac{5}{2}\times 5$$

Combine \frac{5}{2}x and -\frac{5}{2}x to get 0.

$$\frac{1}{2}x^{2}-\frac{5}{2}\times 5$$

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

$$\frac{1}{2}x^{2}+\frac{-5\times 5}{2}$$

Multiply -5 and 5 to get -25.

$$\frac{1}{2}x^{2}+\frac{-25}{2}$$

Fraction \frac{-25}{2} can be rewritten as -\frac{25}{2} by extracting the negative sign.

$$\frac{1}{2}x^{2}-\frac{25}{2}$$