Solve (2k-3)(3+2k)-(3k-5)^2-30k

$$( 2 k - 3 ) ( 3 + 2 k ) - ( 3 k - 5 ) ^ { 2 } - 30 k$$

Evaluate

$$-5k^{2}-34$$

Solution Steps

Use the distributive property to multiply 2k-3 by 3+2k and combine like terms.

$$4k^{2}-9-\left(3k-5\right)^{2}-30k$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3k-5\right)^{2}.

$$4k^{2}-9-\left(9k^{2}-30k+25\right)-30k$$

To find the opposite of 9k^{2}-30k+25, find the opposite of each term.

$$4k^{2}-9-9k^{2}+30k-25-30k$$

Combine 4k^{2} and -9k^{2} to get -5k^{2}.

$$-5k^{2}-9+30k-25-30k$$

Subtract 25 from -9 to get -34.

$$-5k^{2}-34+30k-30k$$

Combine 30k and -30k to get 0.

$$-5k^{2}-34$$

Expand

$$-5k^{2}-34$$

Solution Steps

Use the distributive property to multiply 2k-3 by 3+2k and combine like terms.

$$4k^{2}-9-\left(3k-5\right)^{2}-30k$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3k-5\right)^{2}.

$$4k^{2}-9-\left(9k^{2}-30k+25\right)-30k$$

To find the opposite of 9k^{2}-30k+25, find the opposite of each term.

$$4k^{2}-9-9k^{2}+30k-25-30k$$

Combine 4k^{2} and -9k^{2} to get -5k^{2}.

$$-5k^{2}-9+30k-25-30k$$

Subtract 25 from -9 to get -34.

$$-5k^{2}-34+30k-30k$$

Combine 30k and -30k to get 0.

$$-5k^{2}-34$$