Expand the Expression: Finding (x-x²)² Step by Step

Question

(xx2)2= (x-x^2)^2=

Video Solution

Solution Steps

00:00 Simply
00:03 We'll use the shortened multiplication formulas to open the parentheses
00:12 In this case X is A in the formula
00:19 and X squared is B in the formula
00:26 Therefore we'll substitute in the formula and solve
00:41 Let's solve the multiplications
00:48 And this is the solution to the question

Step-by-Step Solution

To solve the expression (xx2)2(x-x^2)^2, we will use the square of a binomial formula (ab)2=a22ab+b2(a-b)^2 = a^2 - 2ab + b^2.

Let's identify aa and bb in our expression:

  • Here, a=xa = x and b=x2b = x^2.

Applying the formula:

(xx2)2=(x)22(x)(x2)+(x2)2(x - x^2)^2 = (x)^2 - 2(x)(x^2) + (x^2)^2

Calculating each part, we get:

  • (x)2=x2(x)^2 = x^2
  • 2(x)(x2)=2x3-2(x)(x^2) = -2x^3
  • (x2)2=x4(x^2)^2 = x^4

Combining these results, the expression simplifies to:

x42x3+x2x^4 - 2x^3 + x^2

Therefore, the expanded form of (xx2)2(x-x^2)^2 is x42x3+x2\boxed{x^4 - 2x^3 + x^2}.

Answer

x42x3+x2 x^4-2x^3+x^2