how to prove identity 3 that is (a+b) (a-b)=a^2-b^2its for my assignment plase help

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robinmoved's profile pic

robinmoved | Middle School Teacher | (Level 1) Adjunct Educator

Posted on

Are you familiar with FOILing two binomials? 

F=first terms
O=outside terms
I=inside terms
l=last terms

FOIL the expression (a+b)(a-b).

F=(a)*(a)=a^2
O=(a)*(-b)=(-ab)
I=(b)*(a)= (ab)
L=(b)*(-b)=-b^2

You now have a^2-ab+ab-b^2

The middle terms, -ab+ab, cancel.

You are left with a^2-b^2.

 

 

 

sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You need to use the distributive property of multiplication over addition such that:

`(a+b) (a-b) = a(a-b) + b(a-b)`

You need to open the brackets such that:

`(a+b) (a-b) = a^2 - ab + ba - b^2`

By commutative law of multiplication, ab = ba, hence `(a+b) (a-b) = a^2 - ab + ba - b^2 = a^2 - ab +ab - b^2.`

Reducing opposite terms yields:

`(a+b) (a-b) = a^2 - b^2`

Hence, using the distributive property of multiplication over addition yields `(a+b) (a-b) = a^2 - b^2.`

Sources:

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