How would the expression(x^2+4) (y^2+4) be rewritten using two squares?
Answer:
\((xy+4)^2+(2x-2y)^2\)
Step-by-step explanation:
Given: \((x^2+4)(y^2+4)\)
Solution:
Now we rewrite the equation using two squares
\((x^2+2^2)(y^2+2^2)\)
multiply term by term,
\((xy)^2+(2x)^2+(2y)^2+(2.2)^2\)
rearrange the order
\((xy)^2+(2.2)^2+(2y)^2+(2x)^2\)
add and subtract 8xy
\((xy)^2+2(xy)(2.2)+(2.2)^2+(2y)^2-2(2y)(2x)+(2x)^2\)
using formula \((a+b)^2= a^2+2ab+b^2\)
\((xy+4)^2+(2x-2y)^2\)