Math Problem Statement

Square the binomial: (3x + 7)^2

Solution

To solve the problem and square the binomial (3x+7)2(3x + 7)^2, let's expand it step-by-step.

Formula for squaring a binomial:

(a+b)2=a2+2ab+b2(a + b)^2 = a^2 + 2ab + b^2

Here, a=3xa = 3x and b=7b = 7.

  1. Calculate a2a^2: (3x)2=9x2(3x)^2 = 9x^2

  2. Calculate 2ab2ab: 2(3x)(7)=42x2(3x)(7) = 42x

  3. Calculate b2b^2: 72=497^2 = 49

  4. Combine all terms: 9x2+42x+499x^2 + 42x + 49

Final Answer:

The correct choice is: 9x2+42x+49\boxed{9x^2 + 42x + 49}

Do you want more details or have any questions?


Related Questions:

  1. How would the expansion change if the binomial was (3x7)2(3x - 7)^2?
  2. What is the result of squaring (2x+5)2(2x + 5)^2?
  3. How is the binomial formula used in solving quadratic equations?
  4. Can you derive the general pattern for (ax+b)2(ax + b)^2 with different coefficients?
  5. What happens if we cube a binomial instead of squaring it?

Tip:

Always verify your solution by checking each term separately after expanding.

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Math Problem Analysis

Mathematical Concepts

Algebra
Polynomial Expansion
Binomial Theorem

Formulas

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

Theorems

Binomial Theorem

Suitable Grade Level

Grades 8-10