The answer is: " 32a² − 24a − 8 " . __________________________________________________ Given: __________________________________________________ (8a − 8)(4a + 1) ; Let us expand this expression using the: "FOIL" method. ___________________________________________________ "FOIL" stands for "<u>F</u>irst terms, <u>O</u>uter terms, <u> I</u>nner Terms, <u>L</u>ast Terms" ; in that order. ___________________________________________________ Basically: _______________________________________________________ (a + b)(c + d) = ac + ad + bc + bd ;
in which the:
<u>F</u>irst term is: "ac" ; <u>O</u>uter term is: "ad" ; <u>I </u>nner term is: "bc" ; <u>L</u>ast term is: "bd " . __________________________________ So; we have (given):
(8a − 8)(4a + 1) ; __________________________________________________ Let's take the "<u>F</u>irst, <u>O</u>uter, <u></u><u>I</u>nner, and <u>L</u>ast terms" ; as follows: __________________________________________________ <u>F</u>: (8a)*(4a) = 32a² ; __________________________________________________ <u>O</u>: (8a)*(1) = 8a ; __________________________________________________ <u>I </u>: (-8)*(4a) = -32a ; __________________________________________________ <u>L</u>: (-8)*(1) = -8 __________________________________________________ Now, let us write out these terms: __________________________________________________ 32a² + 8a − 32a - 8 ; __________________________________________________ Now, combine the "like terms" in this expression; to simplify:
+ 8a − 32a = -24a ; __________________________________________________ and rewrite the simplified expression ; which is: __________________________________________________ 32a² − 24a − 8 . ______________________________________________________