Question

Simplify (1+x)^3/2-(1+x)^1/2 please explain with steps

Answer 1

Answer:

Step-by-step explanation:

$\sqrt{(1+x)^3} -\sqrt{1+x} \\\\=(1+x)*\sqrt{1+x} -\sqrt{1+x} \\\\=\sqrt{1+x} (1+x-1)\\\\=x\sqrt{1+x}$

Answer 2

Answer:

${(1 + x)}^{ \frac{3}{2} } - {(1 + x)}^{ \frac{1}{2} }$

factorise out (1 + x)^½ :

$= {(1 + x)}^{ \frac{1}{2} }[ ( {1 + x)}^{3} - 1)] \\ = {(1 + x)}^{ \frac{1}{2} } [(1 + 2x + {x}^{2} )(1 + x) - 1] \\ = {(1 + x)}^{ \frac{1}{2} } [(1 + 2x + {x}^{2} + x + 2 {x}^{2} + {x}^{3} ) - 1] \\ = {(1 + x)}^{ \frac{1}{2} } [ {x}^{3} + 3 {x}^{2} + 3x ] \\ { \boxed{= x( {x}^{2} + 3x + 3)(1 + x) {}^{ \frac{1}{2} } }}$