Expand the expression to a polynomial in standard form:

Question

left parenthesis, minus, x, squared, minus, 9, x, minus, 10, right parenthesis, left parenthesis, x, squared, minus, x, minus, 1, right parenthesis
(−x
2
−9x−10)(x
2
−x−1)

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 \((−x^2 − 9x − 10)(x^2 − x − 1)\) and express it in standard form.

1. Distributing each term in \((−x^2 − 9x − 10)\) to each term in \((x^2 − x − 1)\):

   \[ (-x^2)(x^2) + (-x^2)(-x) + (-x^2)(-1) + (-9x)(x^2) + (-9x)(-x) + (-9x)(-1) + (-10)(x^2) + (-10)(-x) + (-10)(-1) \]

2. Calculating each multiplication:

   • \( -x^2 \cdot x^2 = -x^4 \)
   • \( -x^2 \cdot -x = x^3 \)
   • \( -x^2 \cdot -1 = x^2 \)
   • \( -9x \cdot x^2 = -9x^3 \)
   • \( -9x \cdot -x = 9x^2 \)
   • \( -9x \cdot -1 = 9x \)
   • \( -10 \cdot x^2 = -10x^2 \)
   • \( -10 \cdot -x = 10x \)
   • \( -10 \cdot -1 = 10 \)

3. Now we combine all of these products: \[ -x^4 + x^3 + x^2 - 9x^3 + 9x^2 + 9x - 10x^2 + 10x + 10 \]

4. Combine like terms:

   • Combine \(x^3\) terms: \(x^3 - 9x^3 = -8x^3\)
   • Combine \(x^2\) terms: \(x^2 + 9x^2 - 10x^2 = 0\)
   • Combine \(x\) terms: \(9x + 10x = 19x\)
   • The constant term is \(10\).

5. Thus, we get: \[ -x^4 - 8x^3 + 19x + 10 \]

Putting it all together, the final expression in standard form is: \[ \boxed{-x^4 - 8x^3 + 19x + 10} \]