Using the FOIL method, what is #(4x+3)(x+2)#?
2 Answers
Explanation:
FOIL is short for First, Outside, Inside, Last, indicating the various combinations of terms from each of the binomial factors to multiply then add:
#(4x+3)(x+2) = overbrace((4x*x))^"First" + overbrace((4x*2))^"Outside" + overbrace((3*x))^"Inside" + overbrace((3*2))^"Last"#
#=4x^2+8x+3x+6#
#=4x^2+11x+6#
If we did not use FOIL, then we might do the calculation by breaking up each of the factors in turn using distributivity:
#(4x+3)(x+2) = 4x(x+2)+3(x+2)#
#= (4x*x)+(4x*2)+(3*x)+(3*2)#
#= 4x^2+8x+3x+6#
#= 4x^2+11x+6#
So for binomials, FOIL helps you avoid one step.
The main downside of FOIL is that it is limited to binomials.
Explanation:
Letters FOIL in FOIL method stand for First, Outer, Inner, Last and is used to multiply two binomials.
Here we are multiplying
This means first multiply the terms which occur first in each binomial i.e.
Inner means multiply the innermost two terms i.e.
Hence
=
=