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Simplify : a 2 + 10 a + 21 a 2 + 6 a − 7 × a 2 − 1 a + 3 - SSC (English Medium) Class 8 - Mathematics

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Question

Simplify :

\[\frac{a^2 + 10a + 21}{a^2 + 6a - 7} \times \frac{a^2 - 1}{a + 3}\]

Solution

It is known that,

\[a^2  -  b^2  = \left( a + b \right)\left( a - b \right)  ;    a^3  -  b^3  = \left( a - b \right)\left( a^2 + ab + b^2 \right)\]

\[\  \frac{a^2 + 10a + 21}{a^2 + 6a - 7} \times \frac{a^2 - 1}{a + 3}\] 

\[ = \frac{a^2 + 7a + 3a + 21}{a^2 + 7a - a - 7}   \times   \frac{\left( a + 1 \right)\left( a - 1 \right)}{\left( a + 3 \right)}\] 

\[ =   \frac{a\left( a + 7 \right) + 3\left( a + 7 \right)}{a  \left( a + 7 \right) - 1\left( a  + 7 \right)} \times \frac{\left( a + 1 \right)\left( a - 1 \right)}{\left( a + 3 \right)}\] 

\[ =   \frac{\left( a + 7 \right)\left( a + 3 \right)}{\left( a - 1 \right)\left( a + 7 \right)} \times \frac{\left( a + 1 \right)\left( a - 1 \right)}{\left( a + 3 \right)}\] 

\[ =   \left( a + 1 \right)\]

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APPEARS IN

 Balbharati Solution for Balbharati Class 8 Mathematics (2019 to Current)
Chapter 6: Factorisation of Algebraic expressions
Practice Set 6.4 | Q: 2 | Page no. 33
Solution Simplify : a 2 + 10 a + 21 a 2 + 6 a − 7 × a 2 − 1 a + 3 Concept: Factors of A3 - B3.
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