Question
Factorise the following:$12(2x - 3y)^2 - 2x + 3y - 1$
✓
Answer
$12(2x - 3y)^2 - 1(2x - 3y) - 1$
$= 12a^2 - a - 1 [$Taking $(2x - 3y) = a]$
$= 12a^2 - 4a + 3a - 1$
$= 4a(3a - 1) + 1(3a - 1)$
$= (3a - 1)(4a + 1)$
$= [3(2x - 3y) - 1][4(2x - 3y) + 1]$
$= (6x - 9y - 1)(8x - 12y + 1).$
$= 12a^2 - a - 1 [$Taking $(2x - 3y) = a]$
$= 12a^2 - 4a + 3a - 1$
$= 4a(3a - 1) + 1(3a - 1)$
$= (3a - 1)(4a + 1)$
$= [3(2x - 3y) - 1][4(2x - 3y) + 1]$
$= (6x - 9y - 1)(8x - 12y + 1).$
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
Draw the graph of the line $x + y = 5$. Use the graph paper drawn to find the inclination and the $y-$intercept of the line.
→Evaluate the following: $\frac{2 \sin 25^{\circ} \sin 35^{\circ} \sec 55^{\circ} \sec 65^{\circ}}{5 \tan 29^{\circ} \tan 45^{\circ} \tan 61^{\circ}}+\frac{3 \cos 20^{\circ} \cos 50^{\circ} \cot 70^{\circ} \cot 40^{\circ}}{5 \tan 20^{\circ} \tan 50^{\circ} \sin 70^{\circ} \sin 40^{\circ}}$
→Calculate :$(i)\angle ADC(ii)\angle ABC(iii)\angle BAC$
→If $A = 30^\circ ;$show that:$\frac{1+\sin 2 A+\cos 2 A}{\sin A+\cos A}=2 \cos A$
→Solve the following systems of equations by using the method of cross multiplication:
3x + 2y + 25 = 0, 2x + y + 10 = 0
3x + 2y + 25 = 0, 2x + y + 10 = 0
Pooja and Ritu can do a piece of work in $17 \frac{1}{7}$ days. If one day work of Pooja be three fourth of one day work of Ritu' find in how many days each will do the work alone.
→Calculate the amount and the compound interest on:$Rs. 16,000$ in $3$ years, when the rates of the interest for successive years are $10\%, 14\%$ and $15\%$ respectively.
→The mean weight of $60$ students in a class is $40 \ kg$. The mean weight of boys is $50 \ kg$ while that of girls is $30 \ kg$. Find the number of boys and girls in the class.
→Calculate the difference between the simple interest and the compound interest on $Rs. 4,000$ in $2$ years at $8\%$ per annum compounded yearly.
→If $\left(a^2+\frac{1}{a^2}\right)=23$, find the values of: (i) $\left(a+\frac{1}{a}\right)$ (ii) $\left(a^3+\frac{1}{a^3}\right)$.
→