Solve (x-1/3)(x-5/4)

$$(x- \frac{ 1 }{ 3 } )(x- \frac{ 5 }{ 4 } )$$

Evaluate

$$x^{2}-\frac{19x}{12}+\frac{5}{12}$$

Solution Steps

Apply the distributive property by multiplying each term of x-\frac{1}{3} by each term of x-\frac{5}{4}.

$$x^{2}+x\left(-\frac{5}{4}\right)-\frac{1}{3}x-\frac{1}{3}\left(-\frac{5}{4}\right)$$

Combine x\left(-\frac{5}{4}\right) and -\frac{1}{3}x to get -\frac{19}{12}x.

$$x^{2}-\frac{19}{12}x-\frac{1}{3}\left(-\frac{5}{4}\right)$$

Multiply -\frac{1}{3} times -\frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$x^{2}-\frac{19}{12}x+\frac{-\left(-5\right)}{3\times 4}$$

Do the multiplications in the fraction \frac{-\left(-5\right)}{3\times 4}.

$$x^{2}-\frac{19}{12}x+\frac{5}{12}$$

Expand

$$x^{2}-\frac{19x}{12}+\frac{5}{12}$$

Solution Steps

Apply the distributive property by multiplying each term of x-\frac{1}{3} by each term of x-\frac{5}{4}.

$$x^{2}+x\left(-\frac{5}{4}\right)-\frac{1}{3}x-\frac{1}{3}\left(-\frac{5}{4}\right)$$

Combine x\left(-\frac{5}{4}\right) and -\frac{1}{3}x to get -\frac{19}{12}x.

$$x^{2}-\frac{19}{12}x-\frac{1}{3}\left(-\frac{5}{4}\right)$$

Multiply -\frac{1}{3} times -\frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$x^{2}-\frac{19}{12}x+\frac{-\left(-5\right)}{3\times 4}$$

Do the multiplications in the fraction \frac{-\left(-5\right)}{3\times 4}.

$$x^{2}-\frac{19}{12}x+\frac{5}{12}$$