Look at the expression below.
(x+3)2−9
Which of these expressions is an equivalent expression?
Responses
x(x+3)
2x+6
x2
x(x+6)
The equivalent expression to (x+3)2−9 is x(x+6).
To determine which expression is equivalent to (x+3)2−9, we can simplify the given expression step by step and compare it to the options provided.
1. Start with the given expression: (x+3)2−9
2. Expand the squared term: (x+3)(x+3)−9
=> x(x+3) + 3(x+3) − 9
=> x(x) + x(3) + 3(x) + 3(3) − 9
=> x^2 + 3x + 3x + 9 - 9
=> x^2 + 6x
3. Simplify the expression: x^2 + 6x
Comparing this simplified expression to the options provided:
- x(x+3): This expression is different from the simplified form because it includes an additional term (3), so it is not equivalent.
- 2x+6: This expression is different from the simplified form because it is linear (power of x is 1) rather than quadratic (power of x is 2), so it is not equivalent.
- x^2: This expression is different from the simplified form because it is missing the linear term (6x), so it is not equivalent.
- x(x+6): This expression is different from the simplified form because it includes a different constant term (6) instead of the correct constant term (0), so it is not equivalent.
Therefore, the simplified form x^2 + 6x is the correct equivalent expression.
To determine which expression is equivalent to (x+3)² - 9, let's simplify the given expression step by step.
Step 1: Start with the expression (x+3)² - 9.
Step 2: Expand the square by multiplying (x+3) with itself.
(x+3)² = (x+3)(x+3) = x(x+3) + 3(x+3) = x² + 3x + 3x + 9 = x² + 6x + 9
Step 3: Substitute the expanded expression back into the original expression.
(x+3)² - 9 = x² + 6x + 9 - 9 = x² + 6x
Step 4: Simplified expression is x² + 6x.
Comparing this result with the given options, we can see that the expression x² + 6x is equivalent to (x+3)² - 9.