Q. 2 P
Let’s resolve into factors
x2 + 4abx-(a2-b2)2
Answer :
x2 + 4abx-(a2-b2)2 … (1)
(a2-b2)2=[(a + b)2(a-b)2]2
Given, x2 + (p + q)x + pq=(x + p)(x + q) … (2)
Comparing 1 and 2
p + q = 4ab
pq =-(a2-b2)2
we know that (a + b)2=a2 + 2ab + b2 … (3)
similarly, (a-b)2=a2-2ab + b2 … (4)
subtracting 4 from 3
(a + b)2-(a-b)2 =a2 + 2ab + b2-( a2-2ab + b2)
=4ab
∴ (1) can be written as
x2 + (a + b)2x-(a-b)2x-[(a + b)2(a-b)2]2
=[{x + (a + b)2}{x-(a-b)2}]
Apply the formula (a+b)2 = a2 + b2 + 2ab
(a-b)2 = a2 + b2 - 2ab
=[{x + a2 + b2 + 2ab }{x-( a2 + b2 - 2ab )}]
=[{x + a2 + b2 + 2ab }{x- a2 - b2 + 2ab }]
∴ the resolved factors are [{x + a2 + b2 + 2ab }{x- a2 - b2 + 2ab }]
Rate this question :






















I/we factorise the following algebraic expressions:
y2 + 23y + 102
West Bengal - Mathematics
I/we factorise the following algebraic expressions:
a2 + a – 132
West Bengal - Mathematics
I/we factorise the following algebraic expressions:
x2 – x – 6
West Bengal - Mathematics
I/we factorise the following algebraic expressions:
x2 + x – 6
West Bengal - Mathematics
Let’s resolve into factors:
ax2 + (a2 + 1)x + a
West Bengal - Mathematics
Let’s resolve into factors
x2y2 + 23xy-420
West Bengal - Mathematics
Let’s resolve the following algebraic expressions into factors by expressing them as the difference of two squares:
x2-2x-3
West Bengal - Mathematics
Let’s resolve the following algebraic expressions into factors by expressing them as the difference of two squares:
3a2-2a-5
West Bengal - Mathematics
Let’s resolve into factors:
ax2-(a2-2)x-2a
West Bengal - Mathematics
Let’s resolve into factors:
ax2-(a2 + 1)x + a
West Bengal - Mathematics