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

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`

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`