# Extra Questions For Class 9 Maths Chapter 2 | Q1

###### Polynomials | Factorise Polynomials | Algebraic Identities

Question 1: Factorize the given expression: 9x2 + 49y2 + 25z2 - 42xy - 30xz + 70yz

## NCERT Solution to Class 9 Maths

### Explanatory Answer | Chapter 2 Extra Question 1

The coefficient of xy and xz, -42 and -30, are negative and the coefficient of yz, 70, is positive.
So, we can deduce that the coefficient of x is negative and the coefficients of y and z are positive.
Alternatively, the coefficient of x is positive and those of y and z are negative.

#### Compare the given expression to a standard algebraic identity to factorise

The given expression mimics the algebraic identity (a + b + c)2
(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca

9x2 + 49y2 + 25z2 - 42xy - 30xz + 70yz
= (-3x)2 + (7y)2 + (5z)2 + 2(-3x)(7y) + 2(-3x)(5z) + 2(7y)(5z)

(-3x)2 + (7y)2 + (5z)2 + 2(-3x)(7y) + 2(-3x)(5z) + 2(7y)(5z) resembles a2 + b2 + c2 + 2ab + 2bc + 2ca
∴ (-3x)2 + (7y)2 + (5z)2 + 2(-3x)(7y) + 2(-3x)(5z) + 2(7y)(5z) = (-3x + 7y + 5z)2

= (-3x + 7y + 5z)(-3x + 7y + 5z)

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