How to multiply?

Question

Hi.
How do I multiply these:
x(1- sqrt x) * x(1+ sqrt x).
Can you please show me step by step and explain each step?

Answer 1

x (1-sqrt x) * x (1 + sqrt x)
x^2 (1 - sqrt x) (1 + sqrt x) -- reorder elements
x^2 (1 (1 + sqrt x) - sqrt x (1+ sqrt x)) - carry out multiplication
x^2 (1 + sqrt x - sqrtx - (sqrt x * sqrt x)) - regroup
x^2 (1 + (sqrt x - sqrtx) - (x)) - simplify
x^2 (1 + 0 - x) - simplify
x^2 (1 - x) - simplify
x^2 - x^3 - multiply

Answer 2

Step 1: (a + b)(a - b) = a^2 - b^2

So, (1 - sqrt x)(1 + sqrt x) = 1 - (sqrt x)^2 = 1 - x

Step 2: Plug the result of step 1 into your expression
x(1- sqrt x) * x(1+ sqrt x) = x*x*(1 - sqrt x)(1 + sqrt x) =
= x^2 * (1 - x) = x^2 * 1 - x^2 * x = x^2 - x^3

Answer 3

x(1- sqrt x) * x(1+ sqrt x).
(a+b)(a-b) =a^2-b^2
x^2(1-x)
x^2-x^3

Answer 4

First let sqrt x as y

x(1-y) * x(1+y)
= (x-xy)*(x+xy)
=x^2 - x^2y+x^2y-x^2y^2
=x^2-X^2y^2
=(x^2)(1-y^2)


y=sqrt x
y^2 = (sqrt x)^2
= x
therefor,
(x^2)(1-x)= x^2 - x^3