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Asked by Ashish Last Modified
Answer As an experienced tutor registered on UrbanPro.com, I'll guide you through the process of factoring the quadratic expression 100x² – 80xy + 16y². Let's break down the solution into clear steps.
Before factoring, it's essential to recognize the type of quadratic expression we're dealing with. The given expression is a perfect square trinomial, which can be factored using a specific formula.
The expression 100x² – 80xy + 16y² falls under the category of (a - b)², where 'a' and 'b' are terms in the form of ax and by, respectively. The formula for factoring a perfect square trinomial is:
(a−b)2=a2−2ab+b2(a−b)2=a2−2ab+b2
In our case, a=10xa=10x and b=4yb=4y. Applying the formula:
(10x−4y)2=(10x)2−2(10x)(4y)+(4y)2(10x−4y)2=(10x)2−2(10x)(4y)+(4y)2
Now, let's simplify the expression obtained from the formula:
100x2−80xy+16y2100x2−80xy+16y2
=100x2−80xy+16y2=100x2−80xy+16y2
This is the factored form of the given quadratic expression.
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