To determine the equivalent form of the equation \( y = x^2 - 1x - 20 \) from the options provided, let’s first simplify the factored form.
The given factors are:
\[ y = (x + 8)(x + 11) \]
Now, we can expand this expression:
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Multiply \( x + 8 \) by \( x + 11 \): \[ (x + 8)(x + 11) = x^2 + 11x + 8x + 88 \]
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Combine like terms: \[ x^2 + 19x + 88 \]
This means that:
\[ y = (x + 8)(x + 11) \] is equivalent to
\[ y = x^2 + 19x + 88 \].
Now, we will compare with the original equation \( y = x^2 - 1x - 20 \):
To confirm if it’s equivalent, let’s try to factor \( x^2 - 1x - 20 \) to see if it results in the same factors.
To factor \( x^2 - x - 20 \):
- We need two numbers that multiply to \(-20\) (the constant term) and add up to \(-1\) (the coefficient of \(x\)). These numbers are \( -5\) and \(4\).
- Thus, the factorization is: \[ y = (x - 5)(x + 4) \]
Next, we compare:
- The expanded form of \( (x - 5)(x + 4) \) is: \[ x^2 + 4x - 5x - 20 = x^2 - 1x - 20 \]
As we can see, this matches our original equation.
So, we conclude that:
- \( y = x^2 + 19x + 88 \) is equivalent to \( y = (x + 8)(x + 11) \).
- The original equation \( y = x^2 - 1x - 20 \) is a different equation.
Thus, the equivalent match from the original options given is:
Correct option: \( y = x^2 + 19x + 88 \).