For what values of a and b will these two expression be equal?
(a+b)^2
and
a^2 + b^2
0
(a+b)^2=a^2+b^2
a^2+2ab+b^2=a^2+b^2
2ab=0
then: a=0 and b=0
if either a or b is equal to 0,
(a+b)^2 and a^2 + b^2 will have the same values.
To find the values of a and b for which the two expressions are equal, we can set them equal to each other and solve for a and b.
(a+b)^2 = a^2 + b^2
Expanding the left side of the equation:
a^2 + 2ab + b^2 = a^2 + b^2
We can then cancel out the common terms on both sides:
2ab = 0
To solve for a and b, we need to set the expression equal to zero and find the values that satisfy it. Here, we have two possibilities:
1) If a = 0, then the equation becomes:
0 = 0*b
No matter what value b takes, the equation is satisfied, so any value of b will work when a = 0.
2) If b = 0, then the equation becomes:
2a*0 = 0
This equation is satisfied when a is any real number.
Thus, the values of a and b for which the two expressions (a+b)^2 and a^2 + b^2 are equal are:
a can be any real number and b can be any real number or b can be zero, while a can have any value.