Question

How would the expression (x^2+1)(y^2+4) be rewritten using two squares?

Answer 1

I cannot think of another method rather than try them one by one.
D.
(x²+1)(y²2+4)=x²y²+y²+4x²+4
(xy-2)²+(2x+y)²=(x²y²-4xy+4)+(4x²+4xy+y²)=x²y²+4+4x²+y²

Try it this way:
since all the choices group xy and 2 together, we can regroup x²y²+y²+4x²+4 into 
(x²y²+4)+(y²+4x²)
=(x²y²+4-4xy)+(y²+4x²+4xy) or (x²y²+4+4xy)+(y²+4x²-4xy)
=(xy-2)²+(y+2x)² or (xy+2)²+(y-2x)²

Answer 2

The expression D is the correct choice to be rewritten.

What is algebraic expression?

'Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. Any value that is placed before and multiplied by a variable is a coefficient.'

According to the given problem,

Evaluating the given expression:

( x² + 1 )( y² + 4 )

= x²y² + 4x² + y² + 4                      (1)

Now, evaluating option D:

( xy - 2 )² + ( 2x + y )²

= x²y² + 4 - 4xy + 4x² + y² + 4xy

=  x²y² + 4 + 4x² + y² + 4xy - 4xy

⇒  x²y² + 4x² + y² + 4                 (2)

Therefore, the expressions (1) and (2) match.

Hence, the option D is the expression which on evaluating can be rewritten as the given expression.

Learn more about algebraic expressions here:

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