Math Problem Statement

Rewrite without parentheses and simplify. (y + 3)^2

Solution

To simplify (y+3)2(y + 3)^2, we can use the formula for expanding a square of a binomial:

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

Here, a=ya = y and b=3b = 3. Applying the formula:

(y+3)2=y2+2(y)(3)+32(y + 3)^2 = y^2 + 2(y)(3) + 3^2

Simplifying each term:

=y2+6y+9= y^2 + 6y + 9

So, the expression simplifies to:

y2+6y+9y^2 + 6y + 9

Would you like me to explain how to expand other types of expressions?

Here are five related questions to explore further:

  1. How do you expand (y3)2(y - 3)^2?
  2. What is the difference between (y+3)2(y + 3)^2 and (y3)2(y - 3)^2?
  3. How can you factor the expression y2+6y+9y^2 + 6y + 9 back into its original form?
  4. What is the general formula for (a+b)3(a + b)^3?
  5. Can the method of squaring binomials be extended to trinomials?

Tip: Always double-check your expanded form by multiplying the factors back together to ensure accuracy.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Polynomial Expansion
Binomial Theorem

Formulas

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

Theorems

Binomial Expansion

Suitable Grade Level

Grades 8-10