Mathematics

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

2 Answer

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

NEWS TODAY