Respuesta :
The equivalent expressions are:
[tex](x+y)^2 = x^2+2xy+y^2[/tex]
[tex](x+y)^2 = x(x+y)+y(x+y)[/tex]
[tex](x+y)^2 = (x+y)(x+y)[/tex]
[tex](x+y)^2=(y+x)^2[/tex]
Solution:
We have to find the equivalent expression for the given expression
Given expression is:
[tex](x+y)^2[/tex]
First equivalent expression:
Let us first use the algebraic identity
[tex](a+b)^2=a^2+2ab+b^2[/tex]
Therefore,
[tex](x+y)^2 = x^2+2xy+y^2[/tex]
Second Equivalent expression:
From above we get,
[tex](x+y)^2 = x^2+2xy+y^2[/tex]
2xy can be rewritten as xy + xy
Thus we get,
[tex]x^2+2xy + y^2 = x^2+xy+xy+y^2[/tex]
Group the terms we get,
[tex]x^2+2xy + y^2 = (x^2+xy)+(xy+y^2)[/tex]
Factor out "x" from first bracket and "y" from second bracket
[tex]x^2+2xy+y^2 = x(x+y)+y(x+y)[/tex]
Thus the equivalent expression is:
[tex](x+y)^2 = x(x+y)+y(x+y)[/tex]
Third equivalent expression:
[tex]\text{We know that } a^2 = a \times a[/tex]
Therefore,
[tex](x+y)^2 = (x+y)(x+y)[/tex]
Fourth equivalent expression:
By commutative property we know that,
[tex]a + b = b + a[/tex]
Therefore,
[tex](x+y)^2=(y+x)^2[/tex]
Thus the equivalent expressions are found
