Question
Factorize:
$7(x - 2y)^2 - 25(x - 2y) + 12$
$7(x - 2y)^2 - 25(x - 2y) + 12$
✓
Answer
Let $x - 2y = P = 7P^2 - 25P + 12$
Splitting the middle term, $= 7P^2 - 21P - 4P + 12 = 7P(P - 3) - 4(P - 3) = (P - 3)(7P - 4)$
Substituting $P = x - 2y = (x - 2y - 3)(7(x - 2y) - 4) = (x - 2y - 3)(7x - 14y - 4)$
$\therefore$ $7(x - 2y)^2 - 25(x - 2y) + 12$
$= (x - 2y - 3)(7x - 14y - 4)$
Splitting the middle term, $= 7P^2 - 21P - 4P + 12 = 7P(P - 3) - 4(P - 3) = (P - 3)(7P - 4)$
Substituting $P = x - 2y = (x - 2y - 3)(7(x - 2y) - 4) = (x - 2y - 3)(7x - 14y - 4)$
$\therefore$ $7(x - 2y)^2 - 25(x - 2y) + 12$
$= (x - 2y - 3)(7x - 14y - 4)$
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
In figure, ABC is a right angled triangle at A, BCED, ACFG and ABMN are squares on the sides BC, CA and AB respectively. Line segment $\text{AX}\perp\text{DE}$ meets BC at Y.
Show that:
$\text{ar}(\text{BCED})=\text{ar}(\text{ABMN})+\text{ar}(\text{ACFG})$
→Show that:
$\text{ar}(\text{BCED})=\text{ar}(\text{ABMN})+\text{ar}(\text{ACFG})$
In the given figure, m and it are two plane mirrors perpendicular to each other. Show that the incident ray CA is parallel to the reflected ray BD.
If$ a + b + c = 0$, then write the value of $\frac{\text{a}^2}{\text{bc}}+\frac{\text{b}^2}{\text{ca}}+\frac{\text{c}^2}{\text{ab}}.$
→The radius and height of a right circular cone are in the ratio $5 : 12$ and its volume is $2512$ cubic cm. Find the slant height and radius of the cone. $($Use $\pi=3.14).$
→There are 25 persons in a tent which is conical in shape. Every person needs an area of 4 sq.m, of the ground inside the tent. If height of the tent is 18 m , find the volume of the tent.
Given: For the tent,
height $(h)=18 m$,
number of people in the tent $=25$,
area required for each person $=4 sq \cdot m$
To find: Volume of the tent
→Given: For the tent,
height $(h)=18 m$,
number of people in the tent $=25$,
area required for each person $=4 sq \cdot m$
To find: Volume of the tent
If $\frac{\sqrt3-1}{\sqrt3+1}=\text{x}+\text{y}\sqrt3,$ find the value of x and y.
→Find the volume of a conical tank with the following dimensions in liters:
Height $12cm$, slant height $13cm.$
→Height $12cm$, slant height $13cm.$
Factorise:
Prove that $\frac{0.85\times0.85\times0.85+0.15\times0.15\times0.15}{0.85\times0.85-0.85\times0.15+0.15\times0.15}=1$
→Prove that $\frac{0.85\times0.85\times0.85+0.15\times0.15\times0.15}{0.85\times0.85-0.85\times0.15+0.15\times0.15}=1$
Find the median of the data:
15, 6, 16, 8, 22, 21, 9, 18, 25
15, 6, 16, 8, 22, 21, 9, 18, 25
Find $(i)$ the slant height, $(ii)$ the curved surface area and $(iii)$ total surface area of a cone, if its base radius is $12 \ cm$ and height is $16 \ cm. (\pi= 3.14)$
→