Question

If two cubes whose volume are given by (x³+6y²+12z+8)cubic units and (x³-2z+10-y²)cubic unita respectively are melted to form a new cube,find the expression representing the volume of the new cube thus formed​

Answer 1

Step-by-step explanation:

Given that: If two cubes whose volume are given by (x³+6y²+12z+8)cubic units and (x³-2z+10-y²)cubic unit respectively are melted to form a new cube.

To find:find the expression representing the volume of the new cube thus formed.

Solution: We know that ,if two cubes are melted and formed a new cube,than volume of new cube is equal to the sum of volume of melted cubes.

Volume of cube 1:

$V_1 = {x}^{3} + 6 {y}^{2} + 12z + 8\:\:{unit}^3$

Volume of second cube:

$V_2 = {x}^{3} - 2z + 10 - {y}^{2}\:\:{unit}^3$

Volume of new cube= volume of cube1+ volume of cube 2

$V_n = V_1 + V_2$

now,its a simple form of polynomial addition,remember that like terms are added and subtracted in polynomial

$V_n = {x}^{3} + 6 {y}^{2} + 12z + 8 + {x}^{3} - 2z + 10 - {y}^{2} \\ \\ = {x}^{3} + {x}^{3} + 6 {y}^{2} - {y}^{2} + 12z - 2z + 8 + 10 \\ \\V_n = 2 {x}^{3} + 5 {y}^{2} + 10z + 18$

Thus,volume of new cube is

$\bold{V_n = 2 {x}^{3} + 5 {y}^{2} + 10z +18 \:\:{unit}^3}$

Hope it helps you.

Answer 2

Answer:

volume of new cube is=2x³+5y²+10z+18unit 3