Math Problem Statement

(x-3)^2

Solution

The expression (x3)2(x - 3)^2 represents a binomial squared. To expand this, you can apply the formula for the square of a binomial:

(ab)2=a22ab+b2(a - b)^2 = a^2 - 2ab + b^2

In this case, a=xa = x and b=3b = 3, so:

(x3)2=x22(3)(x)+32(x - 3)^2 = x^2 - 2(3)(x) + 3^2

Simplifying:

(x3)2=x26x+9(x - 3)^2 = x^2 - 6x + 9

So, (x3)2=x26x+9(x - 3)^2 = x^2 - 6x + 9.

Would you like more details or have any questions?

Here are 5 related questions for further exploration:

  1. What is the expansion of (x+4)2(x + 4)^2?
  2. How would you expand (2x5)2(2x - 5)^2?
  3. How can you factor x210x+25x^2 - 10x + 25?
  4. What is the general form for (ax+b)2(ax + b)^2?
  5. How do you complete the square for the expression x26xx^2 - 6x?

Tip: When expanding binomials, always apply the square of a binomial formula and simplify step by step.

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Math Problem Analysis

Mathematical Concepts

Algebra
Binomial Expansion

Formulas

(a - b)^2 = a^2 - 2ab + b^2

Theorems

Square of a binomial

Suitable Grade Level

Grades 7-9