E-Math Note : Usage of bracket in Expansion


Another TIP for students taking Elementary Mathematics (E-Math)

Qn: Expand and Simplify the following:

(y+z)^2-(y-z)^2

Method 1 : Expansion using one of the Algebraic rules

(y+z)^2-(y-z)^2</p>
<p>=y^2+2yz+z^2-y^2-2yz+z^2

Did you see what is not right?

Method 2: Recognizing (A)^2 - (B)^2=(A+B)(A-B)

so (y+z)^2-(y-z)^2=(y+z+y-z)(y+z-[y-z])

Method 1:

(y+z)^2-(y-z)^2</p>
<p>=y^2+2yz+z^2-y^2-2yz+z^2

Bracket is missing! the negative sign belongs to the expansion of (y-z)^2 not just y

Correct Ans:

(y+z)^2-(y-z)^2</p>
<p>=y^2+2yz+z^2-(y^2-2yz+z^2)

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