Solve (1)(a-3)(2a+1)-2a(a-5/2)

$$( 1 ) ( a - 3 ) ( 2 a + 1 ) - 2 a ( a - \frac { 5 } { 2 } )$$

Evaluate

$$-3$$

Solution Steps

Use the distributive property to multiply 1 by a-3.

$$\left(a-3\right)\left(2a+1\right)-2a\left(a-\frac{5}{2}\right)$$

Apply the distributive property by multiplying each term of a-3 by each term of 2a+1.

$$2a^{2}+a-6a-3-2a\left(a-\frac{5}{2}\right)$$

Combine a and -6a to get -5a.

$$2a^{2}-5a-3-2a\left(a-\frac{5}{2}\right)$$

Use the distributive property to multiply -2a by a-\frac{5}{2}.

$$2a^{2}-5a-3-2a^{2}-2a\left(-\frac{5}{2}\right)$$

Multiply -2 times -\frac{5}{2}.

$$2a^{2}-5a-3-2a^{2}+5a$$

Combine 2a^{2} and -2a^{2} to get 0.

$$-5a-3+5a$$

Combine -5a and 5a to get 0.

$$-3$$

Factor

$$-3$$