The Difference of Square: a^2 - b^2 = (a + b)(a - b) Sara did a question as: 2x^2 - 2y^2 = (2x + 2y)(2x - 2y).

What's wrong with Sara's work? How to fix it?

Step-by-step explanation:

Given

Difference of two squares:

Sara Solution to a question:

Required

State what's wrong with Sara's work

How to fix it

In Sara's solution, the coefficient of x and y is 2. Sara's solution is wrong because she included the coefficients of x and y when converting the expression to difference of two squares.

To fix this, the very first thing that needs to done is to factorize the given expression (as follows)

Then the difference of two squares can be applied on the expression in bracket. This gives

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2

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