Extra Questions For Class 9 Maths Chapter 2 | Q1

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

Video Explanation

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.
Both answers are correct.

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)