Solve left(x+5/2right)left(x+3/2right)

$$\left( x+ \frac{ 5 }{ 2 } \right) \left( x+ \frac{ 3 }{ 2 } \right)$$

Evaluate

$$x^{2}+4x+\frac{15}{4}$$

Solution Steps

Apply the distributive property by multiplying each term of x+\frac{5}{2} by each term of x+\frac{3}{2}.

$$x^{2}+x\times \frac{3}{2}+\frac{5}{2}x+\frac{5}{2}\times \frac{3}{2}$$

Combine x\times \frac{3}{2} and \frac{5}{2}x to get 4x.

$$x^{2}+4x+\frac{5}{2}\times \frac{3}{2}$$

Multiply \frac{5}{2} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$x^{2}+4x+\frac{5\times 3}{2\times 2}$$

Do the multiplications in the fraction \frac{5\times 3}{2\times 2}.

$$x^{2}+4x+\frac{15}{4}$$

Expand

$$x^{2}+4x+\frac{15}{4}$$

Solution Steps

Apply the distributive property by multiplying each term of x+\frac{5}{2} by each term of x+\frac{3}{2}.

$$x^{2}+x\times \frac{3}{2}+\frac{5}{2}x+\frac{5}{2}\times \frac{3}{2}$$

Combine x\times \frac{3}{2} and \frac{5}{2}x to get 4x.

$$x^{2}+4x+\frac{5}{2}\times \frac{3}{2}$$

Multiply \frac{5}{2} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$x^{2}+4x+\frac{5\times 3}{2\times 2}$$

Do the multiplications in the fraction \frac{5\times 3}{2\times 2}.

$$x^{2}+4x+\frac{15}{4}$$