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How to Simplify (4x2 - 2x) - (-5x2 - 8x) ?

Here is the steps to simply
(4x2 - 2x) - (-5x2 - 8x)
= 4x2 - 2x + 5x2 + 8x.
= 4x2 + 5x2 - 2x + 8x.
= 9x2 + 6x.
= 3x(3x + 2).

The volume of a globe varies as the cube of its radius. Three solid globes of diameters 11/2, 2 and 21/2 metres are melted and formed into a new solid globe. Find the diameter of the new globe.

Solution:

Let V be the volume of a globe of radius R.

Then, by problem,

V ∝ R3

Therefore V = kR3 ..... (1) [k = constant of variation ]

If v1, v2 and v3 cubic metres be the respective volumes of globes having radii ¾, 1 and 5/4 metres then using (1) we get,

v1 = k ∙ (3/4)3 = 27k/64 ;

v2 = k ∙ l3 = k;

v3 = k ∙ (5/4)3 = 125k/64

Let v cubic metre be the volume of the new solid globe. Then,

v = v1 + v2 + v3 or, v = 27k/64 + k + 125k/64

or, v = 216k/64

or, v = 27k/8

If the radius of the new solid globe be r metre, then using (1) we get,

v = kr3

or, kr3 = 27k/8

or, r3 = (3/2)3

or, r = 3/2.

Therefore, the diameter of the new globe = 2r = 2 ∙ 3/2 = 3 metres.