Are the expressions (x+7)(x−3) and (x−3)(x+7) equivalent expressions? Explain.(1 point)
Responses
The expressions are not equivalent because they have different factors.
The expressions are not equivalent because they have different factors.
The expressions are not equivalent because they have different quantities.
The expressions are not equivalent because they have different quantities.
The expressions are equivalent because they have the same factors.
The expressions are equivalent because they have the same factors.
The expressions are equivalent because they have the same number of factors.
The expressions are equivalent because they have the same number of factors.
No, good grief
The expressions are equivalent because they have the same factors. !!!!
The expressions are equivalent because multiplication is cummutative.
Good point :)
The correct answer is: The expressions are equivalent because they have the same factors.
To determine if two expressions are equivalent, we need to multiply out the expressions and simplify them. Let's do that for the given expressions:
Expression 1: (x+7)(x−3)
Multiplying using the distributive property, we get:
x * x + x * (-3) + 7 * x + 7 * (-3)
Simplifying further, we have:
x^2 - 3x + 7x - 21
Combining like terms, we obtain:
x^2 + 4x - 21
Expression 2: (x−3)(x+7)
Again, applying the distributive property, we get:
x * x + x * 7 - 3 * x - 3 * 7
Simplifying gives us:
x^2 + 7x - 3x - 21
Combining like terms, we have:
x^2 + 4x - 21
By comparing the results of both expressions, we can see that they have the same simplified form: x^2 + 4x - 21. Therefore, the expressions (x+7)(x−3) and (x−3)(x+7) are equivalent expressions since they have the same factors when expanded and simplified.