Answered

Consider the expressions below.

A. [tex]11x^2 + 6x - 6[/tex]
B. [tex]7x^2 + 16x + 25[/tex]
C. [tex]11x^2 - 5x + 13[/tex]
D. [tex]7x^2 - 3x + 8[/tex]

For each expression below, select the letter that corresponds to the equivalent expression given above.

1. [tex](x^2 + 15x + 65) + (2x - 5)(3x + 8)[/tex] is equivalent to expression [tex]\square[/tex]

2. [tex](4x + 1)(3x - 4) - (5x^2 - 10x - 12)[/tex] is equivalent to expression [tex]\square[/tex]

3. [tex](8x^2 + 19x + 4) + (3x + 2)(x - 5)[/tex] is equivalent to expression [tex]\square[/tex]

4. [tex](6x + 1)(3x - 7) - (7x^2 - 34x - 20)[/tex] is equivalent to expression [tex]\square[/tex]



Answer :

GinnyAnswer
Let's analyze the given expressions step by step to find their equivalents.

1. For the expression [tex]\(\left(x^2 + 15x + 65\right) + \left(2x - 5\right)\left(3x + 8\right)\)[/tex]:
- Expanding and simplifying, this expression results in [tex]\(7x^2 + 16x + 25\)[/tex].
- Therefore, this is equivalent to expression B.

2. For the expression [tex]\(\left(4x + 1\right)\left(3x - 4\right) - \left(5x^2 - 10x - 12\right)\)[/tex]:
- Expanding and simplifying, this expression results in [tex]\(7x^2 - 3x + 8\)[/tex].
- Therefore, this is equivalent to expression D.

3. For the expression [tex]\(\left(8x^2 + 19x + 4\right) + \left(3x + 2\right)\left(x - 5\right)\)[/tex]:
- Expanding and simplifying, this expression results in [tex]\(11x^2 + 6x - 6\)[/tex].
- Therefore, this is equivalent to expression A.

4. For the expression [tex]\(\left(6x + 1\right)\left(3x - 7\right) - \left(7x^2 - 34x - 20\right)\)[/tex]:
- Expanding and simplifying, this expression results in [tex]\(11x^2 - 5x + 13\)[/tex].
- Therefore, this is equivalent to expression C.

Let's compile the matches:

- [tex]\(\left(x^2 + 15x + 65\right) + \left(2x - 5\right)\left(3x + 8\right)\)[/tex] is equivalent to expression B.
- [tex]\(\left(4x + 1\right)\left(3x - 4\right) - \left(5x^2 - 10x - 12\right)\)[/tex] is equivalent to expression D.
- [tex]\(\left(8x^2 + 19x + 4\right) + \left(3x + 2\right)\left(x - 5\right)\)[/tex] is equivalent to expression A.
- [tex]\(\left(6x + 1\right)\left(3x - 7\right) - \left(7x^2 - 34x - 20\right)\)[/tex] is equivalent to expression C.

Thus, the correct matches are:
- [tex]\(\left(x^2 + 15x + 65\right) + \left(2x - 5\right)\left(3x + 8\right)\)[/tex] is equivalent to expression B.
- [tex]\(\left(4x + 1\right)\left(3x - 4\right) - \left(5x^2 - 10x - 12\right)\)[/tex] is equivalent to expression D.
- [tex]\(\left(8x^2 + 19x + 4\right) + \left(3x + 2\right)\left(x - 5\right)\)[/tex] is equivalent to expression A.
- [tex]\(\left(6x + 1\right)\left(3x - 7\right) - \left(7x^2 - 34x - 20\right)\)[/tex] is equivalent to expression C.

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