Answer
a) The expressions evaluate to 1 and 1.
b) The expressions evaluate to 9 and 5.
c) When x=2 and y=3, the expressions evaluate to 25 and 13.
d) The two expressions are not equal for all values of x and y as shown by the examples given, so the student is incorrect.
Work Step by Step
a) substitute the given values
$(x+y)^2=(1+0)^2=1^2=1$
$x^2+y^2=1^2+0^2=1+0=1$
b) substitute the given values
$(x+y)^2=(1+2)^2=3^2=9$
$x^2+y^2=1^2+2^2=1+4=5$
c) Let x=2 and y=3
$(x+y)^2=(2+3)^2=5^2=25$
$x^2+y^2=2^2+3^2=4+9=13$
d) The claim is not correct because the result of simplifying the equations is not the same for every combination of values for x and y.
