Theory:

Use the following identities to factorize the expressions.
 
a+b2=a2+2ab+b2ab2=a22ab+b2a2b2=(a+b)(ab)a+b3=a3+3a2b+3ab2+b3ab3=a33a2b+3ab2b3a3+b3=(a+b)(a2ab+b2)a3b3=(ab)(a2+ab+b2)
Example:
1) \(y^3+64\)
 
Let us write the above expression as \(y^3+4^3\).
 
Use the identity, \(a^3+b^3 = (a+b)(a^2-ab+b^2)\).
 
y3+43=(y+4)(y2y(4)+42)
 
y3+43=(y+4)(y24y+16)
 
 
2) \(9x^2 -16y^2\)
 
Let us write the above expression as \((3x)^2-(4y)^2\).
 
Use the identity, \(a^2-b^2\) \(=\) \((a+b)(a-b)\).
 
\((3x)^2-(4x)^2\) \(=\) \((3x+4y)(3x-4y)\).