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