a)25a2-49b4
=(5a)2-(7b2)2
=(5a-7b2)(5a+7b2)
b)100a2-9b4
=(10a)2-(3b2)2
=(10a-3b2)(10a+3b2)
c)a4-4b2
=(a2)2-(2b)2
=(a2-2b)(a2+2b)
a) 25a2 - 49b2
= (5a + 7b)(5a - 7b)
b) 100a2 - 9b2
= (10a - 3b)(10a + 3b)
c) a4 - 4b2
= (a2 - 2b)(a2 + 2b)
d) \(\dfrac{4}{9}a^{4^{ }}-\dfrac{25}{4}\)
= \(\left(\dfrac{2}{3}a^2+\dfrac{5}{2}\right)\left(\dfrac{2}{3}a^2-\dfrac{5}{2}\right)\)
e) \(\dfrac{1}{4}a^2-b^2\)
=\(\left(\dfrac{1}{2}a-b\right)\left(\dfrac{1}{2}a+b\right)\)
f) \(\dfrac{1}{4}a^2-\dfrac{1}{9}b^2\)
= \(\left(\dfrac{1}{2}a-\dfrac{1}{3}b\right)\left(\dfrac{1}{2}a+\dfrac{1}{3}b\right)\)
g) \(\dfrac{1}{25}-36x^2\)
= \(\left(\dfrac{1}{5}-6x\right)\left(\dfrac{1}{5}+6x\right)\)
h) \(25a^2-\dfrac{1}{4}b^2\)
= \(\left(5a-\dfrac{1}{2}b\right)\left(5a+\dfrac{1}{2}b\right)\)
