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E-Math Note : Usage of bracket in Expansion

Written on November 20, 2007 by Ai Ling in E-Maths, Learning Tools

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

$(y+z)^2-(y-z)^2 =y^2+2yz+z^2-y^2-2yz+z^2$

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:

$(y+z)^2-(y-z)^2 =y^2+2yz+z^2-y^2-2yz+z^2$

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

Correct Ans:

$(y+z)^2-(y-z)^2 =y^2+2yz+z^2-(y^2-2yz+z^2)$

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