Solve 91(2a+1)^2-4a(2a+1)+4a^2

$$91 ( 2 a + 1 ) ^ { 2 } - 4 a ( 2 a + 1 ) + 4 a ^ { 2 }$$

Evaluate

$$360a^{2}+360a+91$$

Solution Steps

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(2a+1\right)^{2}.

$$91\left(4a^{2}+4a+1\right)-4a\left(2a+1\right)+4a^{2}$$

Use the distributive property to multiply 91 by 4a^{2}+4a+1.

$$364a^{2}+364a+91-4a\left(2a+1\right)+4a^{2}$$

Use the distributive property to multiply -4a by 2a+1.

$$364a^{2}+364a+91-8a^{2}-4a+4a^{2}$$

Combine 364a^{2} and -8a^{2} to get 356a^{2}.

$$356a^{2}+364a+91-4a+4a^{2}$$

Combine 364a and -4a to get 360a.

$$356a^{2}+360a+91+4a^{2}$$

Combine 356a^{2} and 4a^{2} to get 360a^{2}.

$$360a^{2}+360a+91$$

Expand

$$360a^{2}+360a+91$$

Solution Steps

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(2a+1\right)^{2}.

$$91\left(4a^{2}+4a+1\right)-4a\left(2a+1\right)+4a^{2}$$

Use the distributive property to multiply 91 by 4a^{2}+4a+1.

$$364a^{2}+364a+91-4a\left(2a+1\right)+4a^{2}$$

Use the distributive property to multiply -4a by 2a+1.

$$364a^{2}+364a+91-8a^{2}-4a+4a^{2}$$

Combine 364a^{2} and -8a^{2} to get 356a^{2}.

$$356a^{2}+364a+91-4a+4a^{2}$$

Combine 364a and -4a to get 360a.

$$356a^{2}+360a+91+4a^{2}$$

Combine 356a^{2} and 4a^{2} to get 360a^{2}.

$$360a^{2}+360a+91$$