Question

Factorise 1/16x^2y^2-4/49y^2z^2

Answer 1

$\dfrac{1}{x^2y^2} - \dfrac{4}{49y^2z^2}$

combine them into single fraction:

$= \dfrac{49y^2z^2 - 4(x^2y^2)}{(x^2y^2) (49y^2z^2)}}$

Write numerator in the form of a² - b²:

$= \dfrac{(7yz)^2 - (2xy)^2}{ 49x^2y^4z^2}}$

Apply a² - b² = (a + b) (a - b) :

$= \dfrac{(7yz -2 xy)(7yz+ 2xy)}{ 49x^2y^4z^2}}$

Take out 7 as the common factor from the numerator:

$= \dfrac{y(7z -2 x)(7z+ 2x)}{ 49x^2y^4z^2}}$

Divide 7 from both numerator and denominator:

$= \dfrac{(7z -2 x)(7z+ 2x)}{ 49x^2y^3z^2}}$