Question
Factorize:
$a^3x^3 - 3a^2bx^2 + 3ab^2x - b^3$
$a^3x^3 - 3a^2bx^2 + 3ab^2x - b^3$
✓
Answer
$a^3x^3 - 3a^2bx^2 + 3ab^2x - b^3$
$= (ax)^3 - 3(ax)^2 \times b + 3(ax)b^2 - b^3$
$= (ax - b)^3$ $\big[\because$ $a^3 - 3a^2b + 3ab^2 - b^3= (a - b)^3$$\big]$
$= (ax - b)(ax - b)(ax - b)$$\therefore$ $a^3x^3 - 3a^2bx^2 + 3ab^2x - b^3$
$= (ax - b)(ax - b)(ax - b)$
$= (ax)^3 - 3(ax)^2 \times b + 3(ax)b^2 - b^3$
$= (ax - b)^3$ $\big[\because$ $a^3 - 3a^2b + 3ab^2 - b^3= (a - b)^3$$\big]$
$= (ax - b)(ax - b)(ax - b)$$\therefore$ $a^3x^3 - 3a^2bx^2 + 3ab^2x - b^3$
$= (ax - b)(ax - b)(ax - b)$
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
Factorise:
$x^2 + 2xy + y^2 - a^2 + 2ab - b^2$
→$x^2 + 2xy + y^2 - a^2 + 2ab - b^2$
Express the following equation in the form ax + by + c = 0 and indicate the values of a, b, c in case.$\sqrt{2}\text{x}+\sqrt{3}\text{y}=5$
→Find the laterall surface area and total surface area of a cuboid of length $80 cm$ , breadth $40 cm$ and height $20 cm .$
→Factorize:
$2(x+y)^2-9(x+y)-5$
→$2(x+y)^2-9(x+y)-5$
The mean of 200 items was 50. Later on, it was on discovered that the two items were misread as 92 and 8 instead of 192 and 88. Find the correct mean.
Give the possible expression for the length & breadth of the rectangle having $35y^2 - 13y - 12$ as its area.
→Factorise:
$1+b^3+8 c^3-6 b c$
→$1+b^3+8 c^3-6 b c$
Prove that, if a line is perpendicular to one of the two parallel lines, then it is perpendicular to the other line also.
Given: line AB || line CD and line EF intersects them at P and Q respectively.
line EF ⊥ line AB
To prove: line EF ⊥ line CD
Define the following terms:
Parallel lines.
Parallel lines.
If an angle is 30° more than one half of its complement, find the measure of the angle.