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Factorisation by Regrouping Terms

Factors of ...

Question

Factors of $5 y^{2} - 20 y - 8 z + 2 y z$ are

A

(5 y + 2 z)

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B

(5 z + 2 y)

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C

(y + 4)

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D

(y - 4)

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Solution

The correct options are
A $(5 y + 2 z)$
D $(y - 4)$
$5 y^{2} - 20 y - 8 z + 2 y z$
$= 5 y (y - 4) + 2 z (y - 4)$
$= (y - 4) (5 y + 2 z)$

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Q. Factorise the expression:

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Q. Show that each one of the following systems of linear equation is inconsistent:
(i) 2x + 5y = 7
6x + 15y = 13

(ii) 2x + 3y = 5
6x + 9y = 10

(iii) 4x − 2y = 3
6x − 3y = 5

(iv) 4x − 5y − 2z = 2
5x − 4y + 2z = −2
2x + 2y + 8z = −1

(v) 3x − y − 2z = 2
2y − z = −1
3x − 5y = 3

(vi) x + y − 2z = 5
x − 2y + z = −2
−2x + y + z = 4

Q. Which of the following terms in the expression

5 y^{2} - 11 y + 2 y z - 5 z

y

" as a common factor?

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Factorisation by Regrouping Terms

Standard VIII Mathematics

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