76. use the foil method to multiply the binomials: (2x - 5)(3x + 4)6x^2 - 206x^2 - 15x - 206x^2 + 8x - 206x^2 - 7x - 20

6x^2 -7x -20

Step-by-step explanation:

FOIL is a mnemonic to help you remember to multiply each term of one binomial with every term of the other binomial. The mnemonic is only applicable to binomials.

The underlying principle is the distributive property of multiplication over addition. If you look at the pattern, you see that the first term of the first binomial is multiplied by each term of the second. Then the next (second) term of the first binomial is multiplied by each term of the second. This (distributive property) approach works for factors of any length (trinomials or longer, for example).

First terms: (2x - 5)(3x + 4) . . . . 6x^2

Outer terms: (2x - 5)(3x + 4) . . . . 8x

Inner terms: (2x - 5)(3x + 4) . . . . -15x

Last terms: (2x - 5)(3x + 4) . . . . -20

The middle two products from FOIL produce "like terms" that need to be combined to give the final result:

... (2x - 5)(3x + 4) = 6x^2 -7x -20