Question
Solve $x^2+9 y^2-6 x y-25 a^2$
✓
Answer
$x^2+9 y^2-6 x y-25 a^2=\left(x^2-6 x y+9 y^2\right)-25 a^2$
$=\left[x^2-2 x x \times 3 y+(3 y)^2\right]-25 a^2$
$=(x-3 y)^2-(5 a) 2$
$=[(x-3 y)-5 a][(x-3 y)+5 a]$
$=(x-3 y-5 a)(x-3 y+5 a)$
$=\left[x^2-2 x x \times 3 y+(3 y)^2\right]-25 a^2$
$=(x-3 y)^2-(5 a) 2$
$=[(x-3 y)-5 a][(x-3 y)+5 a]$
$=(x-3 y-5 a)(x-3 y+5 a)$
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
A cycle was sold at a gain of 10%. Had it been sold for Rs. 260 more, the gain would have been 14%. Find the cost price of the cycle.
How many soap cakes can be placed in a box of size $56 cm \times 0.4 m \times 0.25 m$, it the size of soap cake is $7 cm \times 5 cm \times 2.5 cm$ ?
→Find the selling price when.
CP = Rs. 875 and loss % = 12%
CP = Rs. 875 and loss % = 12%
A General arranges his soldiers in rows to form a perfect square. He finds that in doing so, 60 soldiers are left out. If the total number of soldiers be 8160, find the number of soldiers in each row.
A man is 10 times older than his grandson. He is also 54 years older than him. Find their present ages.
In the figure, BDEF and DCEF are each a parallelogram. It is true that BD = DC? Why or why not?
Find the square root of the following by prime factorization.1764
How many bricks, each of size 25cm × 13.5cm × 6cm, will be required to build a wall 8m long, 5.4m high and 33cm thick?
Find the squares of the following numbers using column method. Verify the result by finding the square using the usual multiplication,
$71$
→$71$
The following table shows the number of saplings planted by 30 students. Fill in the boxes and find the average number of saplings planted by each student.
→| No. of saplings (Scores) $x_i$ | No. of students (frequency) $f_i$ | $f_i$ × $x_i$ |
| 1 | 4 | 4 |
| 2 | 6 | __ |
| 3 | 12 | __ |
| 4 | 8 | __ |
| N = __ | $\sum f_i \times x_i=$ __ |