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

$$5 a ( 1 + 2 a ) ( 2 a - 1 ) + 2 ( a + 3 ) ( a - 2 ) =$$

Evaluate

$$20a^{3}+2a^{2}-3a-12$$

Solution Steps

Use the distributive property to multiply 5a by 1+2a.

$$\left(5a+10a^{2}\right)\left(2a-1\right)+2\left(a+3\right)\left(a-2\right)$$

Apply the distributive property by multiplying each term of 5a+10a^{2} by each term of 2a-1.

$$10a^{2}-5a+20a^{3}-10a^{2}+2\left(a+3\right)\left(a-2\right)$$

Combine 10a^{2} and -10a^{2} to get 0.

$$-5a+20a^{3}+2\left(a+3\right)\left(a-2\right)$$

Use the distributive property to multiply 2 by a+3.

$$-5a+20a^{3}+\left(2a+6\right)\left(a-2\right)$$

Apply the distributive property by multiplying each term of 2a+6 by each term of a-2.

$$-5a+20a^{3}+2a^{2}-4a+6a-12$$

Combine -4a and 6a to get 2a.

$$-5a+20a^{3}+2a^{2}+2a-12$$

Combine -5a and 2a to get -3a.

$$-3a+20a^{3}+2a^{2}-12$$

Expand

$$20a^{3}+2a^{2}-3a-12$$

Solution Steps

Use the distributive property to multiply 5a by 1+2a.

$$\left(5a+10a^{2}\right)\left(2a-1\right)+2\left(a+3\right)\left(a-2\right)$$

Apply the distributive property by multiplying each term of 5a+10a^{2} by each term of 2a-1.

$$10a^{2}-5a+20a^{3}-10a^{2}+2\left(a+3\right)\left(a-2\right)$$

Combine 10a^{2} and -10a^{2} to get 0.

$$-5a+20a^{3}+2\left(a+3\right)\left(a-2\right)$$

Use the distributive property to multiply 2 by a+3.

$$-5a+20a^{3}+\left(2a+6\right)\left(a-2\right)$$

Apply the distributive property by multiplying each term of 2a+6 by each term of a-2.

$$-5a+20a^{3}+2a^{2}-4a+6a-12$$

Combine -4a and 6a to get 2a.

$$-5a+20a^{3}+2a^{2}+2a-12$$

Combine -5a and 2a to get -3a.

$$-3a+20a^{3}+2a^{2}-12$$