Question

Subtract the given two equations:
3x(x-4y+5z) from 4x(2x-3y+10z)

Answer 1

Hint: There can be two ways to solve this problem, the first one is horizontal subtraction, just take the two given equations and subtract them both placed in horizontal direction, make sure to perform operation only to like terms having the same variables, the second method is explained in later part.

Complete step-by-step answer:

Given equation is
$3x\left( {x - 4y + 5z} \right)$ ............................ (1)
$4x\left( {2x - 3y + 10z} \right)$ ........................ (2)
Now we have to subtract equation (2) from equation (1)
$ \Rightarrow 3x\left( {x - 4y + 5z} \right) - 4x\left( {2x - 3y + 10z} \right)$
Now simplify this equation we have,
$ \Rightarrow 3{x^2} - 12xy + 15xz - 8{x^2} + 12xy - 40xz$
Now collect like terms we have,
$ \Rightarrow \left( {3 - 8} \right){x^2} - \left( {12 - 12} \right)xy + \left( {15 - 40} \right)xz$
Now simplify we have,
$ \Rightarrow - 5{x^2} - \left( 0 \right)xy + \left( {25} \right)xz$
Now as we know that anything multiplied by 0 is zero.
$ \Rightarrow - 5{x^2} + 25xz$.
So this is the required value of the subtraction.

Note: In the second method we can use vertical subtraction, in this the two equations are placed upside down and then like terms coefficients are dealt with to get the answer. Both the methods yield the same answer and anyone of them can be used.