Is (x-5)(x+3) equivalent to 2x^2-x^2-2x-20+5?Explain why
No, (x-5)(x+3) is not equivalent to 2x^2-x^2-2x-20+5.
The correct expansion of (x-5)(x+3) is:
(x-5)(x+3) = x(x) + x(3) - 5(x) - 5(3)
= x^2 + 3x - 5x - 15
= x^2 - 2x - 15
So, the correct expanded form is x^2 - 2x - 15, not 2x^2-x^2-2x-20+5.
No, (x-5)(x+3) is not equivalent to 2x^2-x^2-2x-20+5.
First, let's simplify the expression (x-5)(x+3):
(x-5)(x+3) = x(x+3) - 5(x+3)
= x^2 + 3x - 5x - 15
= x^2 - 2x - 15
On the other hand, let's simplify the given expression: 2x^2 - x^2 - 2x -20 + 5:
2x^2 - x^2 - 2x - 20 + 5 = x^2 - 2x - 15
As we can see, the two simplified expressions, x^2 - 2x - 15, are equivalent. However, the given expression 2x^2 - x^2 - 2x - 20 + 5 is not equivalent to (x-5)(x+3) because it includes additional terms (-20 and +5) which are not present in the simplified expression of (x-5)(x+3).
To determine whether the expressions (x-5)(x+3) and 2x^2 - x^2 - 2x - 20 + 5 are equivalent, we need to simplify both expressions and check if they are equal.
Let's start with (x-5)(x+3):
Using the distributive property, we need to multiply each term in the first expression (x-5) by each term in the second expression (x+3):
(x-5)(x+3) = x(x) + 3(x) - 5(x) - 5(3)
Simplifying further, we get:
= x^2 + 3x - 5x - 15
= x^2 - 2x - 15
Now, let's simplify the expression 2x^2 - x^2 - 2x - 20 + 5:
Combining like terms, we have:
2x^2 - x^2 - 2x - 20 + 5 = (2-1)x^2 - 2x - 20 + 5
= 1x^2 - 2x - 20 + 5
= x^2 - 2x - 15
Comparing this simplified expression to the simplified expression we obtained earlier from (x-5)(x+3), we see that:
(x-5)(x+3) = x^2 - 2x - 15
Therefore, (x-5)(x+3) is indeed equivalent to 2x^2 - x^2 - 2x - 20 + 5.