Question
Simplify:
$(2 x+5 y)(3 x+4 y)-(7 x+3 y)(2 x+y)$
$(2 x+5 y)(3 x+4 y)-(7 x+3 y)(2 x+y)$
✓
Answer
$(2 x+5 y)(3 x+4 y)$
$=2 x(3 x+4 y)+5 y(3 x+4 y)$
$=6 x^{(1+1)}+8 x y+15 y x+20 y^{(1+1)}$
$=6 x^2+23 x y+20 y^2$
$(7 x+3 y)(2 x+y)$
$=7 x(2 x+y)+3 y(2 x+y)$
$=14 x^{(1+1)}+7 x y+6 y x+3 y$
$=14 x^2+13 x y+3 y^2$
$\therefore(2 x+5 y)(3 x+4 y)-(7 x+3 y)(2 x-y)$
$=6 x^2+23 x y+20 y^2-\left(14 x^2+13 x y+3 y^2\right)$
$=6 x^2-14 x^2+23 x y-13 x y+20 y^2-3 y^2$
$=-8 x^2+10 x y+17 y^2$
$=2 x(3 x+4 y)+5 y(3 x+4 y)$
$=6 x^{(1+1)}+8 x y+15 y x+20 y^{(1+1)}$
$=6 x^2+23 x y+20 y^2$
$(7 x+3 y)(2 x+y)$
$=7 x(2 x+y)+3 y(2 x+y)$
$=14 x^{(1+1)}+7 x y+6 y x+3 y$
$=14 x^2+13 x y+3 y^2$
$\therefore(2 x+5 y)(3 x+4 y)-(7 x+3 y)(2 x-y)$
$=6 x^2+23 x y+20 y^2-\left(14 x^2+13 x y+3 y^2\right)$
$=6 x^2-14 x^2+23 x y-13 x y+20 y^2-3 y^2$
$=-8 x^2+10 x y+17 y^2$
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
If x : y = 3 : 4, find (3x + 4y) : (5x + 6y).
Simplify:
$\Big(\frac{3}{11}\times\frac{5}{6}\Big)-\Big(\frac{9}{12}\times\frac{4}{3}\Big)+\Big(\frac{5}{13}\times\frac{6}{15}\Big)$
→$\Big(\frac{3}{11}\times\frac{5}{6}\Big)-\Big(\frac{9}{12}\times\frac{4}{3}\Big)+\Big(\frac{5}{13}\times\frac{6}{15}\Big)$
Arrange the following rational numbers in descending order:
$-2,\frac{-13}{6},\frac{8}{-3},\frac{1}{3}$
→$-2,\frac{-13}{6},\frac{8}{-3},\frac{1}{3}$
A rectangular grassy lawn measuring 38 m by 25 m has been surrounded externally by a 2.5 -m-wide path. Calculate the cost of gravelling the path at the rate of Rs 120 per $m ^2$.
→Solve the following equations. Check your result in case.
0.18(5x - 4) = 0.5x + 0.8
0.18(5x - 4) = 0.5x + 0.8
The inner circumference of a circular track is 330m. The track is 10.5m wide everywhere. Calculate the cost of putting up a fence along the outer circle at the rate of Rs 20 per metre.
In the given figure a rectangular plot of land measures 8m by 6m. In each of the corners, there is a flower bed in the form of a quadrant of a circle of radius 2m. Also, there is a flower bed in the area of the remaining plot.
Write five examples of each one of:
- A cone.
- A sphere.
- A cuboid.
- A cylinder.
By selling an article for Rs. 240, a man makes a profit of 20%. What is his C.P.? What would his profit percent be if he sold the article for Rs. 275?
Construct $\triangle\text{ABC}$ in which AB = 6.4cm, $\angle\text{A}=45^\circ$ and $\angle\text{B}=60^\circ.$
→