Expand the expression to a polynomial in standard form:

Question

left parenthesis, 2, x, squared, minus, x, plus, 3, right parenthesis, left parenthesis, x, squared, minus, 6, x, plus, 2, right parenthesis
(2x
2
−x+3)(x
2
−6x+2)

Solve the problem just like the example below
⬇️
Expand the expression to a polynomial in standard form:
left parenthesis, x, squared, minus, x, minus, 2, right parenthesis, left parenthesis, minus, x, squared, plus, 3, x, minus, 6, right parenthesis
(x
2
−x−2)(−x
2
+3x−6)

minus, x, squared
−x
2
plus, 3, x
+3x
minus, 6
−6
x, squared
x
2
minus, x, to the power 4
−x
4
3, x, cubed
3x
3
minus, 6, x, squared
−6x
2
minus, x
−x
x, cubed
x
3
minus, 3, x, squared
−3x
2
6, x
6x
minus, 2
−2
2, x, squared
2x
2
minus, 6, x
−6x
12
12
Combine like terms:
Combine like terms:
minus, x, to the power 4 , plus, 4, x, cubed, minus, 7, x, squared, plus, 12
−x
4
+4x
3
−7x
2
+12

Answer 1

Let's expand the expression \((2x^2 - x + 3)(x^2 - 6x + 2)\).

1. First, distribute \(2x^2\) across the second polynomial:

   • \(2x^2 \cdot x^2 = 2x^4\)
   • \(2x^2 \cdot (-6x) = -12x^3\)
   • \(2x^2 \cdot 2 = 4x^2\)

2. Next, distribute \(-x\) across the second polynomial:

   • \(-x \cdot x^2 = -x^3\)
   • \(-x \cdot (-6x) = 6x^2\)
   • \(-x \cdot 2 = -2x\)

3. Finally, distribute \(3\) across the second polynomial:

   • \(3 \cdot x^2 = 3x^2\)
   • \(3 \cdot (-6x) = -18x\)
   • \(3 \cdot 2 = 6\)

Now we have: \[ \begin{align*} 2x^4 & + (-12x^3) + (4x^2) \ & + (-x^3) + (6x^2) + (-2x) \ & + (3x^2) + (-18x) + 6 \end{align*} \]

Now let's combine all of the like terms:

• For \(x^4\): \(2x^4\)
• For \(x^3\): \(-12x^3 - x^3 = -13x^3\)
• For \(x^2\): \(4x^2 + 6x^2 + 3x^2 = 13x^2\)
• For \(x\): \(-2x - 18x = -20x\)
• Constant term: \(6\)

So, after combining like terms, we get: \[ 2x^4 - 13x^3 + 13x^2 - 20x + 6 \]

Thus, the final answer in standard form is: \[ \boxed{2x^4 - 13x^3 + 13x^2 - 20x + 6} \]