Solve (28a^3-28a^2+7a)div7a

$$( 28 a ^ { 3 } - 28 a ^ { 2 } + 7 a ) \div 7 a$$

Evaluate

$$\left(a\left(2a-1\right)\right)^{2}$$

Solution Steps

Divide each term of 28a^{3}-28a^{2}+7a by 7 to get a-4a^{2}+a\times \left(2a\right)^{2}.

$$\left(a-4a^{2}+a\times \left(2a\right)^{2}\right)a$$

Use the distributive property to multiply a-4a^{2}+a\times \left(2a\right)^{2} by a.

$$a^{2}-4a^{3}+\left(2a\right)^{2}a^{2}$$

Expand \left(2a\right)^{2}.

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

Calculate 2 to the power of 2 and get 4.

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

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

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

Expand

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

Solution Steps

Divide each term of 28a^{3}-28a^{2}+7a by 7 to get a-4a^{2}+a\times \left(2a\right)^{2}.

$$\left(a-4a^{2}+a\times \left(2a\right)^{2}\right)a$$

Use the distributive property to multiply a-4a^{2}+a\times \left(2a\right)^{2} by a.

$$a^{2}-4a^{3}+\left(2a\right)^{2}a^{2}$$

Expand \left(2a\right)^{2}.

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

Calculate 2 to the power of 2 and get 4.

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

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

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