Question
Factorise:
$2(x+y)^2-9(x+y)-5$
$2(x+y)^2-9(x+y)-5$
✓
Answer
Let $x+y=z$
Then, $2(x+y)^2-9(x+y)-5$
$=2 z^2-9 z-5$
$=2 z^2-10 z+z-5$
$=2 z(z-5)+1(z-5)$
$=(z-5)(2 z+1)$
Now, replacing $z$ by $(x+y)$, we get
$2(x+y)^2-9(x+y)-5$
$=[(x+y)-5][(2(x+y)+1)]$
$=(x+y-5)(2 x+2 y+1)$
Then, $2(x+y)^2-9(x+y)-5$
$=2 z^2-9 z-5$
$=2 z^2-10 z+z-5$
$=2 z(z-5)+1(z-5)$
$=(z-5)(2 z+1)$
Now, replacing $z$ by $(x+y)$, we get
$2(x+y)^2-9(x+y)-5$
$=[(x+y)-5][(2(x+y)+1)]$
$=(x+y-5)(2 x+2 y+1)$
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
Give the geometric representations of the following equations:
- On the number line.
- On the Cartesain plane.
Three angles of a quadrilateral are respectively equal to 110°, 50° and 40°. Find its fourth angle.
How many pairs of adjacent angles are formed when two lines intersect in a point?
In each of the following determine rational numbers a and b:$\frac{\sqrt3-1}{\sqrt3+1}=\text{a}-\text{b}\sqrt3$
→The angles of a quadrilateral are in the ratio 3 : 5 : 9 : 13. Find all the angles of the quadrilateral.
Give the geometric representations of the following equations:
- On the number line.
- On the Cartesain plane.
If the areas of three adjacent face of a cuboid are $8\ cm^3, 18\ cm^3$ and $25\ cm^3$. Find the volume of the cuboid.
→Factorise:$10\Big(3\text{x}+\frac{1}{\text{x}}\Big)^2-\Big(3\text{x}+\frac{1}{\text{x}}\Big)-3$
→Evaluate the following using identities:
$991 \times 1009$
→$991 \times 1009$
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: 
$\triangle\text{MBC}\cong\triangle\text{ABD}$
→$\triangle\text{MBC}\cong\triangle\text{ABD}$