factorise using algebraic identity.
36x^2y^2-25
Answers
Answer:
factorize an algebraic expression expressible as the difference of two squares, we use the following identity a2 - b2 = (a + b) (a – b).
Solution:
64 - x2
= (8)2 - x2, since we know 64 = 8 times 8 which is 82
2.Now by using the formula of a2 - b2 = (a + b)(a – b) to complete the factor fully.
= (8 + x)(8 - x).
3a2 - 27b2
Solution:
3a2 - 27b2
= 3(a2 – 9b2), here we took 3 as common.
=3[(a)2 – (3b)2], since we know 9b2 = 3b times 3b which is (3b)2
So, now we need to apply the formula of a2 - b2 = (a + b)(a – b) to complete the factor fully.
= 3(a + 3b)(a – 3b)
x3 - 25x
Solution:
x3 - 25x
= x(x2 - 25), here we took x as common.
= x(x2 - 52), since we know, 25 = 52
Now we can write x2 – 52 as using the formula of a2 - b2 = (a + b)(a – b).
= x(x + 5)(x - 5).
2. Factor the expressions:
(i) 81a2 - (b - c)2
Solution:
We can write 81a2 - (b - c)2 as a2 - b2
= (9a)2 - (b - c)2, since we know, 81a2 = (9a)2
Now using the formula of a2 – b2 = (a + b) (a – b) we get,
= [9a + (b – c)] [9a - (b – c)]
= [9a + b – c] [9a - b + c ]
36x^2y^2
=(6xy)^2
25=5^2
Now, according to the identity that
a^2-b^2=(a+b)(a-b),
We have,
(6xy)^2-5^2
=(6xy+5)(6xy-5)
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