Question

factorise the following 25 x square + 4 y square + 9square -20 X Y + 12 Y Z - 30 x z

Answer 1

Answer:

( - 5x + 2y + 3z)²

Step-by-step explanation:

25x² + 4y² + 9z² - 20xy + 12yz - 30xz

Note: Whenever three perfect squares and 6 terms are given, just consider the identity

a² + b² + c² + 2ab + 2bc + 2ca

Here, given expression can be written as

(5x)² + (2y)² + (3z)² - 2(5x)(2y) + 2(2y)(3z) - 2(3z)(5x)

If you'll compare last three term with last three terms of the identity, you'll observe that terms 2ab and 2ca are negative ( - 20xy and - 30xz) , in both of these terms (x) is common, so we can say coefficient of x is negative hence

(-5x)² + (2y)² + (3z)² + 2(-5x)(2y) + 2(2y)(3z) + 2(3z)(-5x)

= ( - 5x + 2y + 3z)²       [∵a² + b² + c² + 2ab + 2bc + 2ca = (a + b + c)² ]