how to factorise algebraic expressions containing common binomials
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Factorization of algebraic expressions when a binomial is a common factor:
The expression is written as the product of binomial and the quotient obtained by dividing the given expression is by its binomial.
Solved examples when a binomial is a common factor:
1. Factorize the expression (3x + 1)2 – 5(3x + 1)
Solution:
(3x + 1)2 – 5(3x + 1)
The two terms in the above expression are (3x + 1)2 and 5(3x + 1)
= (3x + 1) (3x + 1) – 5(3x + 1)
Here, we observe that the binomial (3x + 1) is common to both the terms.
= (3x + 1) [(3x + 1) – 5]; [taking common (3x + 1)]
= (3x + 1) (3x - 4)
Therefore, (3x + 1) and (3x - 4) are two factors of the given algebraic expression.
The expression is written as the product of binomial and the quotient obtained by dividing the given expression is by its binomial.
Solved examples when a binomial is a common factor:
1. Factorize the expression (3x + 1)2 – 5(3x + 1)
Solution:
(3x + 1)2 – 5(3x + 1)
The two terms in the above expression are (3x + 1)2 and 5(3x + 1)
= (3x + 1) (3x + 1) – 5(3x + 1)
Here, we observe that the binomial (3x + 1) is common to both the terms.
= (3x + 1) [(3x + 1) – 5]; [taking common (3x + 1)]
= (3x + 1) (3x - 4)
Therefore, (3x + 1) and (3x - 4) are two factors of the given algebraic expression.
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14(3y-5z)^3+7(3y-5z)^2
what
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2min
14 (3y -5z) 3 + 7 (3y-5z) 2 = (3y-5z)2 {14(3y-5z) +7} =(3y-5z)2{42y -70z +7}
= 7 (3y-5z)2(6y -10z +1) (Ans)
= 7 (3y-5z)2(6y -10z +1) (Ans)
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