Question

Which polynomial is equivalent to (2h − 3k)(h + 5k)?

A) 2h2 + 7hk − 15k2

B) 2h2 − 7hk − 15k2

C) 2h2 + 7hk + 15k2

D) 2h2 − 7hk + 15k2

Answer 1

2h^2 + 7hk  -15k^2
you can use factoring

Answer 2

Answer:

Option (a) is correct.

An equivalent polynomial to the given polynomial $\left(2h\:−\:3k\right)\left(h\:+\:5k\right)$ is $2h^2+7hk-15k^2$

Step-by-step explanation:

Given : Polynomial $\left(2h\:−\:3k\right)\left(h\:+\:5k\right)$

We have to find an equivalent polynomial to the given polynomial $\left(2h\:−\:3k\right)\left(h\:+\:5k\right)$

Consider the given polynomial $\left(2h\:−\:3k\right)\left(h\:+\:5k\right)$

Apply FOIL method, $\left(a+b\right)\left(c+d\right)=ac+ad+bc+bd$

$a=2h,\:b=-3k,\:c=h,\:d=5k$

$=2hh+2h\cdot \:5k+\left(-3k\right)h+\left(-3k\right)\cdot \:5k$

Apply plus minus rule, $+(-a)=-a$

$=2hh+2\cdot \:5hk-3hk-3\cdot \:5kk$

Add similar terms, we have,

$\:10hk-3hk=7hk$

We have,

$=2h^2+7hk-15k^2$

Thus, An equivalent polynomial to the given polynomial $\left(2h\:−\:3k\right)\left(h\:+\:5k\right)$ is $2h^2+7hk-15k^2$