Find the Following Product: (3x − 4y + 5z) (9x2 +16y2 + 25z2 + 12xy −15zx + 20yz) - Mathematics

Find the following product:

(3x − 4y + 5z) (9x2 +16y2 + 25z2 + 12xy −15zx + 20yz)

Solution

In the given problem, we have to find Product of equations

Given (3x − 4y + 5z) (9x2 +16y2 + 25z2 + 12xy −15zx + 20yz)

We shall use the identity

x^3 + y^3 + z^3 -xyz = (x+ y +z)(x^2 + y^2+z^2 - xy - yz -zx)

 = (3x)^3 + (-4y)^3 + (5z)^3 - 3 (3x)(4y) (5z)

=  (3x)xx (3x)xx(3x) - (-4y) xx (-4y) xx (-4y)+(5z)xx (5z)xx(5z) -3 (3x) (-4y)(5z)

 = 27x^3 - 64y^3 + 125z^3 + 180xyz

Hence the product of (3x − 4y + 5z) (9x2 +16y2 + 25z2 + 12xy −15zx + 20yz)is  27x^3 - 64y^3 + 125z^3 + 180xyz

Is there an error in this question or solution?

APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 4 Algebraic Identities
Exercise 4.5 | Q 1.4 | Page 28