Rewrite without gibberish text and simplify. y + 6 squared
The Correct Answer and Explanation is:
Expression:
(y + 6)²
Correct Answer:
(y + 6)² = y² + 12y + 36
Explanation
The expression (y + 6)² means that you are multiplying (y + 6) by itself. This is an example of squaring a binomial. A binomial is simply an algebraic expression with two terms, and squaring means raising it to the power of 2.
Here’s how you expand it step by step: (y+6)2=(y+6)(y+6)(y + 6)^2 = (y + 6)(y + 6)
Now apply the distributive property (also known as the FOIL method for binomials):
- First: y×y=y2y \times y = y^2
- Outer: y×6=6yy \times 6 = 6y
- Inner: 6×y=6y6 \times y = 6y
- Last: 6×6=366 \times 6 = 36
Now, add all the terms together: y2+6y+6y+36y^2 + 6y + 6y + 36
Combine like terms: y2+12y+36y^2 + 12y + 36
So, the simplified and correct expanded form of (y + 6)² is: y2+12y+36y^2 + 12y + 36
This follows a well-known formula in algebra: (a+b)2=a2+2ab+b2(a + b)^2 = a^2 + 2ab + b^2
In this case, a = y and b = 6, so:
- a2=y2a^2 = y^2
- 2ab=2⋅y⋅6=12y2ab = 2 \cdot y \cdot 6 = 12y
- b2=62=36b^2 = 6^2 = 36
Thus: (y+6)2=y2+12y+36(y + 6)^2 = y^2 + 12y + 36
Understanding how to expand binomials like this is essential in algebra and helps in solving quadratic equations, graphing parabolas, and simplifying expressions in higher-level math.
