Solve (x+1/4)(-3/4x+2)

$$( x + \frac { 1 } { 4 } ) ( - \frac { 3 } { 4 } x + 2 )$$

Evaluate

$$-\frac{3x^{2}}{4}+\frac{29x}{16}+\frac{1}{2}$$

Solution Steps

Apply the distributive property by multiplying each term of x+\frac{1}{4} by each term of -\frac{3}{4}x+2.

$$x\left(-\frac{3}{4}\right)x+2x+\frac{1}{4}\left(-\frac{3}{4}\right)x+\frac{1}{4}\times 2$$

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

$$x^{2}\left(-\frac{3}{4}\right)+2x+\frac{1}{4}\left(-\frac{3}{4}\right)x+\frac{1}{4}\times 2$$

Multiply \frac{1}{4} times -\frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$x^{2}\left(-\frac{3}{4}\right)+2x+\frac{1\left(-3\right)}{4\times 4}x+\frac{1}{4}\times 2$$

Do the multiplications in the fraction \frac{1\left(-3\right)}{4\times 4}.

$$x^{2}\left(-\frac{3}{4}\right)+2x+\frac{-3}{16}x+\frac{1}{4}\times 2$$

Fraction \frac{-3}{16} can be rewritten as -\frac{3}{16} by extracting the negative sign.

$$x^{2}\left(-\frac{3}{4}\right)+2x-\frac{3}{16}x+\frac{1}{4}\times 2$$

Combine 2x and -\frac{3}{16}x to get \frac{29}{16}x.

$$x^{2}\left(-\frac{3}{4}\right)+\frac{29}{16}x+\frac{1}{4}\times 2$$

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

$$x^{2}\left(-\frac{3}{4}\right)+\frac{29}{16}x+\frac{2}{4}$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$x^{2}\left(-\frac{3}{4}\right)+\frac{29}{16}x+\frac{1}{2}$$

Expand

$$-\frac{3x^{2}}{4}+\frac{29x}{16}+\frac{1}{2}$$

Solution Steps

Apply the distributive property by multiplying each term of x+\frac{1}{4} by each term of -\frac{3}{4}x+2.

$$x\left(-\frac{3}{4}\right)x+2x+\frac{1}{4}\left(-\frac{3}{4}\right)x+\frac{1}{4}\times 2$$

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

$$x^{2}\left(-\frac{3}{4}\right)+2x+\frac{1}{4}\left(-\frac{3}{4}\right)x+\frac{1}{4}\times 2$$

Multiply \frac{1}{4} times -\frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$x^{2}\left(-\frac{3}{4}\right)+2x+\frac{1\left(-3\right)}{4\times 4}x+\frac{1}{4}\times 2$$

Do the multiplications in the fraction \frac{1\left(-3\right)}{4\times 4}.

$$x^{2}\left(-\frac{3}{4}\right)+2x+\frac{-3}{16}x+\frac{1}{4}\times 2$$

Fraction \frac{-3}{16} can be rewritten as -\frac{3}{16} by extracting the negative sign.

$$x^{2}\left(-\frac{3}{4}\right)+2x-\frac{3}{16}x+\frac{1}{4}\times 2$$

Combine 2x and -\frac{3}{16}x to get \frac{29}{16}x.

$$x^{2}\left(-\frac{3}{4}\right)+\frac{29}{16}x+\frac{1}{4}\times 2$$

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

$$x^{2}\left(-\frac{3}{4}\right)+\frac{29}{16}x+\frac{2}{4}$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$x^{2}\left(-\frac{3}{4}\right)+\frac{29}{16}x+\frac{1}{2}$$