Question
Factorize the following expressions: $a^3 + 3a^2b + 3ab^2 + b^3 - 8$
✓
Answer
$=(a+b)^3-8\left[\therefore a^3+3 a^2 b+3 a b^2+b^3=(a+b) 3\right]$
$=(a+b)^3-23=(a+b-2)\left((a+b)^2+(a+b) \times 2+2^2\right)$
$=(a+b-2)\left(a^2+2 a b+b^2+2 a+2 b+4\right)$
$\therefore a^3+3 a^2 b+3 a b^2+b^3-8$
$=(a+b-2)\left(a^2+2 a b+b^2+2 a+2 b+4\right)$
$=(a+b)^3-23=(a+b-2)\left((a+b)^2+(a+b) \times 2+2^2\right)$
$=(a+b-2)\left(a^2+2 a b+b^2+2 a+2 b+4\right)$
$\therefore a^3+3 a^2 b+3 a b^2+b^3-8$
$=(a+b-2)\left(a^2+2 a b+b^2+2 a+2 b+4\right)$
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 $\sqrt{3}=1.732,\sqrt{5}=2.236,\sqrt{6}=2.449$ and $\sqrt{10}=3.162,$ find to three places of decimal, the value of the following:
$\frac{1}{4\sqrt{3}-3\sqrt{5}}$
→$\frac{1}{4\sqrt{3}-3\sqrt{5}}$
Factorize the following expressions: $32a^3 + 108b^3$
→The sum of two angles of a triangle is $116^\circ $ and their differance is $24^\circ $. Find the measure of each angle of the triangle.
→Show that: $\Big(\frac{1}{\text{x}^{\text{a}-\text{b}}}\Big)^{\frac{1}{\text{a}-\text{c}}}\Big(\frac{1}{\text{x}^{\text{b}-\text{c}}}\Big)^{\frac{1}{\text{b}-\text{a}}}\Big(\frac{1}{\text{x}^{\text{c}-\text{a}}}\Big)^{\frac{1}{\text{c}-\text{b}}}=1$
→Water in a rectangular reservoir having base $80\ m$ by $60\ m$ is $6.5\ m$ deep. In what time can the water be pumped by a pipe of which the cross-section is a square of side $20\ cm$ if the water runs through the pipe at the rate of $15\ km/hr.$
→The angles of a triangles are in the ratio $2 : 3 : 4$ Find the angles.
→The area of a trapezium is $475 cm^2$ and its height is $19 cm$ . Find the lengths of its parallel sides if one side is $4 cm$ greater than the other.
→In figure $POQ$ is a line. Ray $OR$ is perpendicular to line $PQ$. $OS$ is another ray lying between rays $OP$ and $OR$. Prove that $\angle\text{ROS}=\frac{1}{2}(\angle\text{QOS}-\angle\text{POS}).$
→Find the product. $(x - y - z)(x^2 + y^2 + z^2 + xy - yz + xz)$
→If $a + b + c = 9$ and $ab + bc + ca = 26$, find $a^2 + b^2 + c^2.$
→