Question

what should be added to the following algebraic expressions to make them perfect squares trinomials 100x^2-100xy+100y^2​

Answer 1

Answer:

Step-by-step explanation:

100x²-100xy+100y²

= (10x)​² + (10y)²  - (10x)(10y)

but we know that the  a²+ b² - 2ab = (a-b)² which is a perfect square.

comparing (10x)​² + (10y)²  - (10x)(10y)  with equation of form a²+ b² - 2ab,

we can see that we need add another xy coeffecient = 10x*(-10y) = - 100xy

=> (10x)​² + (10y)²  - 100xy - 100xy

=> (10x)​² + (10y)² - 200xy

=> (10x - 10y)² which is a perfect square.

Thus the expression to be added is   (-100)xy.