Question
Simplify the following products:$(\text{x}^3 -3\text{x}^2-\text{x})(\text{x}^2-3\text{x} + 1)$
✓
Answer
In the given problem, we have to find product of $(\text{x}^3 -3\text{x}^2-\text{x})(\text{x}^2-3\text{x} + 1)$
taking x as common factor $\text{x}(\text{x}^2 -3\text{x}-1)(\text{x}^2-3\text{x} + 1)$$(\text{x}^3 -3\text{x}^2-\text{x})(\text{x}^2-3\text{x} + 1)\\=\Big[\text{x}\big(\text{x}^2-3\text{x}-1\big)\big(\text{x}^2-3\text{x}+1\big)\Big]$
$=\text{x}\Big[\big\{\big(\text{x}^2-3\text{x}\big)-1\big\}\big\{\big(\text{x}^2-3\text{x}\big)+1\big\}\Big]$
We shall use the identity $(\text{x}-\text{y})(\text{x}+\text{y})=\text{x}^2-\text{y}^2$$\big(\text{x}^3-3\text{x}^2-\text{x}\big)\big(\text{x}^2-3\text{x}+1\big)\\=\text{x}\Big[\big(\text{x}^2-3\text{x}\big)^2-1^2\Big]$
$=\text{x}\big(\text{x}^4-6\text{x}^3+9\text{x}^2-1\big)$
$=\text{x}^5-6\text{x}^4+9\text{x}^3-\text{x}$
Hence the value of $(\text{x}^3 -3\text{x}^2-\text{x})(\text{x}^2-3\text{x} + 1)$ is $\text{x}^5-6\text{x}^4+9\text{x}^3-\text{x}.$
taking x as common factor $\text{x}(\text{x}^2 -3\text{x}-1)(\text{x}^2-3\text{x} + 1)$$(\text{x}^3 -3\text{x}^2-\text{x})(\text{x}^2-3\text{x} + 1)\\=\Big[\text{x}\big(\text{x}^2-3\text{x}-1\big)\big(\text{x}^2-3\text{x}+1\big)\Big]$
$=\text{x}\Big[\big\{\big(\text{x}^2-3\text{x}\big)-1\big\}\big\{\big(\text{x}^2-3\text{x}\big)+1\big\}\Big]$
We shall use the identity $(\text{x}-\text{y})(\text{x}+\text{y})=\text{x}^2-\text{y}^2$$\big(\text{x}^3-3\text{x}^2-\text{x}\big)\big(\text{x}^2-3\text{x}+1\big)\\=\text{x}\Big[\big(\text{x}^2-3\text{x}\big)^2-1^2\Big]$
$=\text{x}\big(\text{x}^4-6\text{x}^3+9\text{x}^2-1\big)$
$=\text{x}^5-6\text{x}^4+9\text{x}^3-\text{x}$
Hence the value of $(\text{x}^3 -3\text{x}^2-\text{x})(\text{x}^2-3\text{x} + 1)$ is $\text{x}^5-6\text{x}^4+9\text{x}^3-\text{x}.$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
It being given that $\sqrt{2}=1.414,\sqrt{3}=1.732,\sqrt{5}=2.236$ and $\sqrt{10}=3.162,$ find the value of three places of decimals, of the following:$\frac{\sqrt{10}-\sqrt{5}}{\sqrt{2}}$
→It being given that $\sqrt{2}=1.414,\sqrt{3}=1.732,\sqrt{5}=2.236$ and $\sqrt{10}=3.162,$ find the value of three places of decimals, of the following:$\frac{2-\sqrt{3}}{\sqrt{3}}$
→If$ x = 1$ and $y = 6$ is a solution of the equation $8x - ay + a^2 = 0$, find the values of a
→A cube of $9cm$ edge is immersed completely in a rectangular vessel containing water. If the dimensions of the base are $15cm$ and $12cm$, find the rise in water level in the vessel.
→In the given figure ABCD is a cyclic quadrilateral. If $\angle\text{BCD}=100^\circ$ and $\angle\text{ABD}=70^\circ,$ find $\angle\text{ADB}.$
→Diagonals of a parallelogram WXYZ intersect each other at point O. If ∠XYZ∠ = 135°, then measure of ∠XWZ and ∠YZW? If l(OY) = 5 cm, then l(WY) = ?
A rectangular container, whose base is a square of side 5cm, stands on a horizontal table, and holds water up to 1cm from the top. When a solid cube is placed in the water it is completely submerged, the water rises to the top and 2 cubic cm of water overflows. Calculate the volume of the cube and also the length of its edge.
How many pairs of adjacent angles, in all, can you name in figure 10.36.
If ∆XYZ ~ ∆LMN, write the corresponding angles of the two triangles and also write the ratios of corresponding sides.
In figure 3.7, bisectors of ∠B and ∠C of D ABC intersect at point P.
Prove that ∠BPC = 90 + $\frac{1}{2}$ ∠BAC.
→Prove that ∠BPC = 90 + $\frac{1}{2}$ ∠BAC.
