Solve -(3a-2)^2+(a-1)^2

$$- ( 3 a - 2 ) ^ { 2 } + ( a - 1 ) ^ { 2 }$$

Evaluate

$$\left(3-4a\right)\left(2a-1\right)$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(3a-2\right)^{2}.

$$-\left(9a^{2}-12a+4\right)+\left(a-1\right)^{2}$$

To find the opposite of 9a^{2}-12a+4, find the opposite of each term.

$$-9a^{2}+12a-4+\left(a-1\right)^{2}$$

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

$$-9a^{2}+12a-4+a^{2}-2a+1$$

Combine -9a^{2} and a^{2} to get -8a^{2}.

$$-8a^{2}+12a-4-2a+1$$

Combine 12a and -2a to get 10a.

$$-8a^{2}+10a-4+1$$

Add -4 and 1 to get -3.

$$-8a^{2}+10a-3$$

Expand

$$-8a^{2}+10a-3$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(3a-2\right)^{2}.

$$-\left(9a^{2}-12a+4\right)+\left(a-1\right)^{2}$$

To find the opposite of 9a^{2}-12a+4, find the opposite of each term.

$$-9a^{2}+12a-4+\left(a-1\right)^{2}$$

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

$$-9a^{2}+12a-4+a^{2}-2a+1$$

Combine -9a^{2} and a^{2} to get -8a^{2}.

$$-8a^{2}+12a-4-2a+1$$

Combine 12a and -2a to get 10a.

$$-8a^{2}+10a-4+1$$

Add -4 and 1 to get -3.

$$-8a^{2}+10a-3$$