Math Problem Statement

Express (x + 3)^2 as a trinomial in standard form.

Solution

To express (x+3)2(x + 3)^2 as a trinomial, you need to expand it using the formula for the square of a binomial, which is:

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

Here, a=xa = x and b=3b = 3. Let's apply this:

(x+3)2=x2+2(x)(3)+32(x + 3)^2 = x^2 + 2(x)(3) + 3^2

Simplifying:

x2+6x+9x^2 + 6x + 9

So, the trinomial form of (x+3)2(x + 3)^2 is:

x2+6x+9x^2 + 6x + 9

Would you like further details or have any other questions?

Here are 5 related questions for practice:

  1. What is the result of (x4)2(x - 4)^2?
  2. How would you expand (2x+5)2(2x + 5)^2?
  3. Can you expand (x+7)2(x + 7)^2 using the same method?
  4. What is the simplified form of (3x+2)2(3x + 2)^2?
  5. How does the middle term change when squaring a binomial with a negative second term?

Tip: Always remember the middle term comes from doubling the product of the two terms in the binomial!

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Math Problem Analysis

Mathematical Concepts

Algebra
Binomials
Polynomials

Formulas

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

Theorems

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Suitable Grade Level

Grades 7-9