To complete the table, we need to use a* a=a^2, and the FOIL Method.
Expression
(Expression)(Expression)
FOIL Method
(Expression)^2
x+5
(x+5)(x+5)
(x)(x)+(x)(5)+(5)(x)+(5)(5)
x^2+10x+25
3y+1
(3y+1)(3y+1)
(3y)(3y)+(3y)(1)+(1)(3y)+(1)(1)
9y^2+6y+1
z+q
(z+q)(z+q)
(z)(z)+(z)(q)+(q)(z)+(q)(q)
z^2+2zq+q^2
Let's remove the intermediate steps.
Expression
(Expression)^2
x+5
x^2+10x+25
3y+1
9y^2+6y+1
z+q
z^2+2zq+q^2
b
Consider the example below.
( z+ q)^2= z^2+ 2 z q+ q^2
We see that the square of the sum of two terms are equal to the sum of the square of the first term and the second term plus twice the product of them. This also applies to other examples.
c
Let's find an equivalent expression for the square of the sum a+b.
