Solve a^2(2a+6b-7)+a(2a^2-6ab+a)

$$a ^ { 2 } ( 2 a + 6 b - 7 ) + a ( 2 a ^ { 2 } - 6 a b + a )$$

Evaluate

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

Solution Steps

Use the distributive property to multiply a^{2} by 2a+6b-7.

$$2a^{3}+6a^{2}b-7a^{2}+a\left(2a^{2}-6ab+a\right)$$

Use the distributive property to multiply a by 2a^{2}-6ab+a.

$$2a^{3}+6a^{2}b-7a^{2}+2a^{3}-6ba^{2}+a^{2}$$

Combine 2a^{3} and 2a^{3} to get 4a^{3}.

$$4a^{3}+6a^{2}b-7a^{2}-6ba^{2}+a^{2}$$

Combine 6a^{2}b and -6ba^{2} to get 0.

$$4a^{3}-7a^{2}+a^{2}$$

Combine -7a^{2} and a^{2} to get -6a^{2}.

$$4a^{3}-6a^{2}$$

Expand

$$4a^{3}-6a^{2}$$

Solution Steps

Use the distributive property to multiply a^{2} by 2a+6b-7.

$$2a^{3}+6a^{2}b-7a^{2}+a\left(2a^{2}-6ab+a\right)$$

Use the distributive property to multiply a by 2a^{2}-6ab+a.

$$2a^{3}+6a^{2}b-7a^{2}+2a^{3}-6ba^{2}+a^{2}$$

Combine 2a^{3} and 2a^{3} to get 4a^{3}.

$$4a^{3}+6a^{2}b-7a^{2}-6ba^{2}+a^{2}$$

Combine 6a^{2}b and -6ba^{2} to get 0.

$$4a^{3}-7a^{2}+a^{2}$$

Combine -7a^{2} and a^{2} to get -6a^{2}.

$$4a^{3}-6a^{2}$$