Answer:
a. [tex]x^{2} +3x+1[/tex]
b. [tex]x^{2} +5x+6[/tex]
c. [tex]a^{2} +7a+12[/tex]
d. [tex]a^{2} +a-6[/tex]
e. [tex]x^{2} +2x-15[/tex]
f. [tex]x^{2} -3x-10[/tex]
g. [tex]x^{2} -5x+6[/tex]
h. [tex]a^{2} -9a+18[/tex]
Step-by-step explanation:
The process used to multiply two expressions can be remembered by thinking FOIL.
F = first term of each expression multiplied together
O = outermost term of each expression multiplied together
I = innermost term of each expression multiplied together
L= last term of each expression multiplied together
After finding each part of FOIL, the terms are added together.
a. (x+2)(x+1)
F = x*x = [tex]x^{2}[/tex]
O = x*1 = x
I = 2*x = 2x
L = 2*1 = 2
The expression becomes [tex]x^{2} +x+2x+1=x^{2} +3x+1[/tex]
b. (x+2)(x+3)
F = x*x = [tex]x^{2}[/tex]
O = x*3 = 3x
I = 2*x = 2x
L = 2*3 = 6
The expression becomes [tex]x^{2} +3x+2x+6=x^{2} +5x+6[/tex]
c. (a+3)(a+4)
F = a*a = [tex]a^{2}[/tex]
O = a*4 = 4a
I = 3*a = 3a
L = 3*4= 12
The expression becomes [tex]a^{2} +4a+3a+12=a^{2} +7a+12[/tex]
d. (a+3)(a-2)
F = a*a = [tex]a^{2}[/tex]
O = a*(-2) = -2a
I = 3*a = 3a
L = 3*(-2) = -6
The expression becomes [tex]a^{2}-2a+3a-6 =a^{2} +a-6[/tex]
e. (x-3)(x+5)
F = x*x = [tex]x^{2}[/tex]
O = x*5 = 5x
I = (-3)*x = -3x
L = (-3)*5 = -15
The expression becomes [tex]x^{2} +5x-3x-15=x^{2} +2x-15[/tex]
f. (x+2)(x-5)
F = x*x = [tex]x^{2}[/tex]
O = x*(-5) = -5x
I = 2*x = 2x
L = 2*(-5) = -10
The expression becomes [tex]x^{2} -5x+2x-10=x^{2} -3x-10[/tex]
g. (x-3)(x-2)
F = x*x = [tex]x^{2}[/tex]
O = x*(-2) = -2x
I = x*(-3) = -3x
L = (-3)*(-2) = 6
The expression becomes [tex]x^{2} -2x-3x+6=x^{2} -5x+6[/tex]
h. (a-6)(a-3)
F = a*a = [tex]a^{2}[/tex]
O = a*(-3) = -3a
I = (-6)*a = -6a
L = (-6)*(-3) = 18
The expression becomes [tex]a^{2} -3a-6a+18 = a^{2} -9a+18[/tex]
