Math Problem Statement

Expand (2x + 1)^2.

Solution

The problem is to expand (2x+1)2(2x + 1)^2.

Solution:

We use the binomial expansion formula: (a+b)2=a2+2ab+b2(a + b)^2 = a^2 + 2ab + b^2

Here, a=2xa = 2x and b=1b = 1.

  1. Compute a2a^2: (2x)2=4x2(2x)^2 = 4x^2

  2. Compute 2ab2ab: 2(2x)(1)=4x2(2x)(1) = 4x

  3. Compute b2b^2: 12=11^2 = 1

  4. Add them together: 4x2+4x+14x^2 + 4x + 1

Final Answer:

(2x+1)2=4x2+4x+1(2x + 1)^2 = 4x^2 + 4x + 1

Would you like further explanation or to see similar examples?


Here are 5 related questions for practice:

  1. Expand (3x+2)2(3x + 2)^2.
  2. Expand (x4)2(x - 4)^2.
  3. Expand (5x+3)2(5x + 3)^2 and simplify.
  4. Verify the expansion of (2x+1)2(2x + 1)^2 using direct multiplication.
  5. Expand (2x1)2(2x - 1)^2.

Tip: Always check your expansion by re-multiplying the terms for accuracy.

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Math Problem Analysis

Mathematical Concepts

Algebra
Binomial Expansion
Polynomials

Formulas

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

Theorems

Binomial Theorem

Suitable Grade Level

Grades 8-10