Algebraic Expressions and Identities — Maths STD 8 — Question
Maharashtra BoardEnglish MediumSTD 8MathsAlgebraic Expressions and Identities3 Marks
Question
Simplify the following using the identities:
$\frac{198×198−102×102}{96}$
✓
Answer
Let us consider the following expression:
$\frac{198×198−102×102}{96}=\frac{198^2-102^2}{96}$
Using the identity $(a+b)(a-b)=a^2-b^2$
we get:
$\frac{198×198−102×102}{96}=\frac{198^2-102^2}{96}\\=\frac{(198+102)(198−102)}{96}$
$\Rightarrow\frac{198×198−102×102}{96}=\frac{(198+102)(198−102)}{96}$
$\Rightarrow\frac{198×198−102×102}{96}=\frac{300×96}{96}$
$\Rightarrow\frac{198×198−102×102}{96}=300$
Thus, the answer is 300.
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