Discover a wealth of knowledge at Westonci.ca, where experts provide answers to your most pressing questions. Get quick and reliable solutions to your questions from knowledgeable professionals on our comprehensive Q&A platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
To rewrite the given polynomial in its simplest form, we'll proceed through the following steps:
1. Expand the terms inside the expression:
Given expression:
[tex]\[ \left(3x^2 + 9x + 6\right) - \left(8x^2 + 3x - 10\right) + \left(2x + 4\right)\left(3x - 7\right) \][/tex]
2. Distribute and combine like terms:
First, distribute the subtraction:
[tex]\[ \left(3x^2 + 9x + 6\right) - 8x^2 - 3x + 10 + \left(2x + 4\right)\left(3x - 7\right) \][/tex]
3. Expand the product:
Next, expand \(\left(2x + 4\right)\left(3x - 7\right):
[tex]\[ (2x \cdot 3x) + (2x \cdot -7) + (4 \cdot 3x) + (4 \cdot -7) \][/tex]
[tex]\[ = 6x^2 - 14x + 12x - 28 \][/tex]
[tex]\[ = 6x^2 - 2x - 28 \][/tex]
4. Substitute back into the expression:
Now place the expanded product back into the original expression:
[tex]\[ 3x^2 + 9x + 6 - 8x^2 - 3x + 10 + 6x^2 - 2x - 28 \][/tex]
5. Combine like terms:
Combine the \(x^2\) terms:
[tex]\[ 3x^2 - 8x^2 + 6x^2 = (3 - 8 + 6)x^2 = 1x^2 \][/tex]
Combine the \(x\) terms:
[tex]\[ 9x - 3x - 2x = (9 - 3 - 2)x = 4x \][/tex]
Combine the constant terms:
[tex]\[ 6 + 10 - 28 = 6 + 10 - 28 = -12 \][/tex]
6. Write the final expression:
Combine all like terms to get the final simplified polynomial:
[tex]\[ x^2 + 4x - 12 \][/tex]
Therefore, the correct answer is:
[tex]\( \boxed{x^2 + 4x - 12} \)[/tex]
1. Expand the terms inside the expression:
Given expression:
[tex]\[ \left(3x^2 + 9x + 6\right) - \left(8x^2 + 3x - 10\right) + \left(2x + 4\right)\left(3x - 7\right) \][/tex]
2. Distribute and combine like terms:
First, distribute the subtraction:
[tex]\[ \left(3x^2 + 9x + 6\right) - 8x^2 - 3x + 10 + \left(2x + 4\right)\left(3x - 7\right) \][/tex]
3. Expand the product:
Next, expand \(\left(2x + 4\right)\left(3x - 7\right):
[tex]\[ (2x \cdot 3x) + (2x \cdot -7) + (4 \cdot 3x) + (4 \cdot -7) \][/tex]
[tex]\[ = 6x^2 - 14x + 12x - 28 \][/tex]
[tex]\[ = 6x^2 - 2x - 28 \][/tex]
4. Substitute back into the expression:
Now place the expanded product back into the original expression:
[tex]\[ 3x^2 + 9x + 6 - 8x^2 - 3x + 10 + 6x^2 - 2x - 28 \][/tex]
5. Combine like terms:
Combine the \(x^2\) terms:
[tex]\[ 3x^2 - 8x^2 + 6x^2 = (3 - 8 + 6)x^2 = 1x^2 \][/tex]
Combine the \(x\) terms:
[tex]\[ 9x - 3x - 2x = (9 - 3 - 2)x = 4x \][/tex]
Combine the constant terms:
[tex]\[ 6 + 10 - 28 = 6 + 10 - 28 = -12 \][/tex]
6. Write the final expression:
Combine all like terms to get the final simplified polynomial:
[tex]\[ x^2 + 4x - 12 \][/tex]
Therefore, the correct answer is:
[tex]\( \boxed{x^2 + 4x - 12} \)[/tex]
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.