Answer :

Answer:

[tex]12a^2-9a[/tex]

Step-by-step explanation:

FOIL Method

Recall the FOIL method that's used when two factors that are each the sums/differences of two terms, are being multiplied to each other.

  • The first terms of the left and rightmost factors are multiplied together

(the leftmost terms in each factor)

  • The outer term of the leftmost factor is multiplied by the rightmost's outer term

(the leftmost term of the left factor and the rightmost term of the right factor)

  • The inner term of the leftmost factor is multiplied by the rightmost's inner term

(the rightmost term of the left factor and the leftmost of the right factor)

  • The last terms of the left and rightmost factors are multiplied together

(the rightmost terms in each factor)

After all terms are multiplied with each other they are added and simplified for a final answer.

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Applying the Method

  • The first terms of the given problem are 2a and 3, that gives us 6a.
  • The outer terms are 2a and -4a, that gives [tex]\rm -8a^2[/tex]
  • The inner terms are -5a and 3, that gives -15a
  • The last terms are -5a and -4a, that gives [tex]\rm 20a^2[/tex]

When multiplying terms, elements that are alike (i.e. [tex]\rm a[/tex] terms and integers), are multiplied together before they each multiply together ("joining" together without a space).

Adding and simplifying the multiplied terms our final answer is,

[tex]\rm 6a-8a^2-15a+20a^2\\\\\implies-9a+12a^2\:or\: \boxed{12a^2-9a}[/tex].

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