Solve (2a-1)quad(1+2a)-2(a-2)^2

$$( 2 a - 1 ) \quad ( 1 + 2 a ) - 2 ( a - 2 ) ^ { 2 }$$

Evaluate

$$2a^{2}+8a-9$$

Solution Steps

Use the distributive property to multiply 2a-1 by 1+2a and combine like terms.

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

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

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

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

$$4a^{2}-1-2a^{2}+8a-8$$

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

$$2a^{2}-1+8a-8$$

Subtract 8 from -1 to get -9.

$$2a^{2}-9+8a$$

Expand

$$2a^{2}+8a-9$$

Solution Steps

Use the distributive property to multiply 2a-1 by 1+2a and combine like terms.

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

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

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

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

$$4a^{2}-1-2a^{2}+8a-8$$

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

$$2a^{2}-1+8a-8$$

Subtract 8 from -1 to get -9.

$$2a^{2}-9+8a$$