Math Problem Statement

 (x+2)(x+5)

Solution

To expand the expression (x+2)(x+5)(x + 2)(x + 5), use the distributive property (also known as the FOIL method for binomials):

(x+2)(x+5)=x(x+5)+2(x+5)(x + 2)(x + 5) = x(x + 5) + 2(x + 5)

Now, distribute each term:

=x2+5x+2x+10= x^2 + 5x + 2x + 10

Finally, combine the like terms:

=x2+7x+10= x^2 + 7x + 10

So, the expanded form of (x+2)(x+5)(x + 2)(x + 5) is:

x2+7x+10x^2 + 7x + 10

Would you like more details on any of the steps?

Here are some related questions for further practice:

  1. Expand (x+3)(x+6)(x + 3)(x + 6).
  2. Simplify (x4)(x+7)(x - 4)(x + 7).
  3. Factor x2+6x+8x^2 + 6x + 8.
  4. Expand (2x+3)(x1)(2x + 3)(x - 1).
  5. Find the product of (x5)(x+9)(x - 5)(x + 9).

Tip: When expanding binomials, always remember to distribute each term of the first binomial to every term of the second binomial!

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Math Problem Analysis

Mathematical Concepts

Algebra
Binomial Expansion
Distributive Property

Formulas

(a+b)(c+d) = ac + ad + bc + bd

Theorems

Distributive Property

Suitable Grade Level

Grades 7-9