Question
What is (3x + 8)^2 subtracted from 5x - 2
Answers
Answer
What is (3x + 2)^2 subtracted from 3x^2 + 8
Answer
(-3x -1)(2x^2 + 8x +1)
Answered by
GPT-4o mini
To find the expression where \((3x + 8)^2\) is subtracted from \(5x - 2\), you can write it as:
\[
(5x - 2) - (3x + 8)^2
\]
First, let's calculate \((3x + 8)^2\).
\[
(3x + 8)^2 = (3x + 8)(3x + 8) = 9x^2 + 24x + 24x + 64 = 9x^2 + 48x + 64
\]
Now, substitute this back into the original expression:
\[
(5x - 2) - (9x^2 + 48x + 64)
\]
Distributing the negative sign gives us:
\[
5x - 2 - 9x^2 - 48x - 64
\]
Now, combine like terms:
\[
-9x^2 + (5x - 48x) + (-2 - 64)
\]
This simplifies to:
\[
-9x^2 - 43x - 66
\]
So, the final expression is:
\[
-9x^2 - 43x - 66
\]
\[
(5x - 2) - (3x + 8)^2
\]
First, let's calculate \((3x + 8)^2\).
\[
(3x + 8)^2 = (3x + 8)(3x + 8) = 9x^2 + 24x + 24x + 64 = 9x^2 + 48x + 64
\]
Now, substitute this back into the original expression:
\[
(5x - 2) - (9x^2 + 48x + 64)
\]
Distributing the negative sign gives us:
\[
5x - 2 - 9x^2 - 48x - 64
\]
Now, combine like terms:
\[
-9x^2 + (5x - 48x) + (-2 - 64)
\]
This simplifies to:
\[
-9x^2 - 43x - 66
\]
So, the final expression is:
\[
-9x^2 - 43x - 66
\]
Answered by
GPT-4o mini
To find the expression where \((3x + 2)^2\) is subtracted from \(3x^2 + 8\), you can write it as:
\[
(3x^2 + 8) - (3x + 2)^2
\]
First, let's calculate \((3x + 2)^2\):
\[
(3x + 2)^2 = (3x + 2)(3x + 2) = 9x^2 + 12x + 12x + 4 = 9x^2 + 12x + 4
\]
Now, substitute this back into the original expression:
\[
(3x^2 + 8) - (9x^2 + 12x + 4)
\]
Distributing the negative sign gives:
\[
3x^2 + 8 - 9x^2 - 12x - 4
\]
Now, combine like terms:
1. The \(x^2\) terms: \(3x^2 - 9x^2 = -6x^2\)
2. The \(x\) terms: \(0x - 12x = -12x\)
3. The constant terms: \(8 - 4 = 4\)
So, combining all of these, we get:
\[
-6x^2 - 12x + 4
\]
Thus, the final expression is:
\[
-6x^2 - 12x + 4
\]
\[
(3x^2 + 8) - (3x + 2)^2
\]
First, let's calculate \((3x + 2)^2\):
\[
(3x + 2)^2 = (3x + 2)(3x + 2) = 9x^2 + 12x + 12x + 4 = 9x^2 + 12x + 4
\]
Now, substitute this back into the original expression:
\[
(3x^2 + 8) - (9x^2 + 12x + 4)
\]
Distributing the negative sign gives:
\[
3x^2 + 8 - 9x^2 - 12x - 4
\]
Now, combine like terms:
1. The \(x^2\) terms: \(3x^2 - 9x^2 = -6x^2\)
2. The \(x\) terms: \(0x - 12x = -12x\)
3. The constant terms: \(8 - 4 = 4\)
So, combining all of these, we get:
\[
-6x^2 - 12x + 4
\]
Thus, the final expression is:
\[
-6x^2 - 12x + 4
\]
Answered by
GPT-4o mini
To multiply the expression \((-3x - 1)(2x^2 + 8x + 1)\), you can use the distributive property (also known as the FOIL method for binomials). Each term in the first polynomial is multiplied by each term in the second polynomial.
We will distribute \(-3x\) and \(-1\) to the terms in \((2x^2 + 8x + 1)\):
1. **Multiply \(-3x\) by each term:**
\[
-3x \cdot 2x^2 = -6x^3
\]
\[
-3x \cdot 8x = -24x^2
\]
\[
-3x \cdot 1 = -3x
\]
2. **Multiply \(-1\) by each term:**
\[
-1 \cdot 2x^2 = -2x^2
\]
\[
-1 \cdot 8x = -8x
\]
\[
-1 \cdot 1 = -1
\]
Now, combine all the results:
\[
-6x^3 - 24x^2 - 3x - 2x^2 - 8x - 1
\]
Next, combine like terms:
- The \(x^2\) terms: \(-24x^2 - 2x^2 = -26x^2\)
- The \(x\) terms: \(-3x - 8x = -11x\)
Thus, the expression simplifies to:
\[
-6x^3 - 26x^2 - 11x - 1
\]
So, the final result is:
\[
-6x^3 - 26x^2 - 11x - 1
\]
We will distribute \(-3x\) and \(-1\) to the terms in \((2x^2 + 8x + 1)\):
1. **Multiply \(-3x\) by each term:**
\[
-3x \cdot 2x^2 = -6x^3
\]
\[
-3x \cdot 8x = -24x^2
\]
\[
-3x \cdot 1 = -3x
\]
2. **Multiply \(-1\) by each term:**
\[
-1 \cdot 2x^2 = -2x^2
\]
\[
-1 \cdot 8x = -8x
\]
\[
-1 \cdot 1 = -1
\]
Now, combine all the results:
\[
-6x^3 - 24x^2 - 3x - 2x^2 - 8x - 1
\]
Next, combine like terms:
- The \(x^2\) terms: \(-24x^2 - 2x^2 = -26x^2\)
- The \(x\) terms: \(-3x - 8x = -11x\)
Thus, the expression simplifies to:
\[
-6x^3 - 26x^2 - 11x - 1
\]
So, the final result is:
\[
-6x^3 - 26x^2 - 11x - 1
\]