Question
Factorize:
2(x + y)2 - 9(x + y) - 5
2(x + y)2 - 9(x + y) - 5
✓
Answer
Let x + y = z
= 2z2 - 9z - 5
Splitting the middle term,
= 2z2 - 10z + z - 5
= 2z(z - 5) + 1(z - 5)
= (z - 5)(2z + 1)
Substituting z = x + y
= (x + y - 5)(2(x + y) + 1)
= (x + y - 5)(2x + 2y + 1)
$\therefore$ 2(x + y)2 - 9(x + y) - 5 = (x + y - 5)(2x + 2y + 1)
= 2z2 - 9z - 5
Splitting the middle term,
= 2z2 - 10z + z - 5
= 2z(z - 5) + 1(z - 5)
= (z - 5)(2z + 1)
Substituting z = x + y
= (x + y - 5)(2(x + y) + 1)
= (x + y - 5)(2x + 2y + 1)
$\therefore$ 2(x + y)2 - 9(x + y) - 5 = (x + y - 5)(2x + 2y + 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
What do you understand by the word “statistics” in:
Singular form.
Singular form.
Factorise:
1 + 2ab - (a2 + b2)
1 + 2ab - (a2 + b2)
Using factor theorem, show that g(x) is a factor of p(x), when
p(x) = 2x3 + 9x2 - 11x - 30, g(x) = x + 5
p(x) = 2x3 + 9x2 - 11x - 30, g(x) = x + 5
Which of the following figures lie on the same base and between the same parallels. In such a case, write the common base and two parallels:
Factorise:
$\text{x}^2+5\sqrt{5}\text{x}+30$
→$\text{x}^2+5\sqrt{5}\text{x}+30$
A vessel in the form of a hemispherical bowl is full of water. Its contents are emptied in a right circular cylinder. The internal radii of the bowl and the cylinder are 3.5cm and 7cm respectively. Find the height to which the water will rise in the cylinder.
If arcs AXB and CYD of a circle are congruent, find the ratio of AB and CD.
How many bullets can be made out of a cube of lead, whose edge measures 22cm, each bullet being 2cm in diameter?
Write the following in the expanded form:
(a + 2b + c)2
(a + 2b + c)2
Check the following are solutions of the equation 2x - y = 6 and which are not:
(3, 0)
(3, 0)