Answer:
Option (a) is correct.
An equivalent polynomial to the given polynomial [tex]\left(2h\:−\:3k\right)\left(h\:+\:5k\right)[/tex] is [tex]2h^2+7hk-15k^2[/tex]
Step-by-step explanation:
Given : Polynomial [tex]\left(2h\:−\:3k\right)\left(h\:+\:5k\right)[/tex]
We have to find an equivalent polynomial to the given polynomial [tex]\left(2h\:−\:3k\right)\left(h\:+\:5k\right)[/tex]
Consider the given polynomial [tex]\left(2h\:−\:3k\right)\left(h\:+\:5k\right)[/tex]
Apply FOIL method, [tex]\left(a+b\right)\left(c+d\right)=ac+ad+bc+bd[/tex]
[tex]a=2h,\:b=-3k,\:c=h,\:d=5k[/tex]
[tex]=2hh+2h\cdot \:5k+\left(-3k\right)h+\left(-3k\right)\cdot \:5k[/tex]
Apply plus minus rule, [tex]+(-a)=-a[/tex]
[tex]=2hh+2\cdot \:5hk-3hk-3\cdot \:5kk[/tex]
Add similar terms, we have,
[tex]\:10hk-3hk=7hk[/tex]
We have,
[tex]=2h^2+7hk-15k^2[/tex]
Thus, An equivalent polynomial to the given polynomial [tex]\left(2h\:−\:3k\right)\left(h\:+\:5k\right)[/tex] is [tex]2h^2+7hk-15k^2[/tex]
