The greatest common factor is the biggest number taken from the values.
Q1. The answer is A. 5y^6
[tex]20 y^{9} +5 y^{6}= 4*5 y^{9}+5 y^{6}[/tex]
Since [tex]x^{a}* x^{b} =x^{a+b} [/tex], then [tex] x^{9}= x^{3}* x^{6} [/tex]
Back to our expression:
[tex]4*5 y^{9}+5 y^{6}=4*5 y^{3}*y^{6}+5 y^{6}=4 y^{3}*5y ^{6}+ 5y ^{6}*1=5 y^{6} (4y ^{3} +1)[/tex]
The greatest common factor is thus [tex]5 y^{6}[/tex]
Q2. The answer is D. 12xy^2
[tex]12x y^{5}+60 x^{4} y^{2} -24 x^{3} y^{3}=12x y^{5}+5*12 x^{4} y^{2} -2*12 x^{3} y^{3}[/tex]
We will use the rule [tex]x^{a}* x^{b} =x^{a+b} [/tex] to factorise the exponents:
[tex]12x y^{5}+5*12 x^{4} y^{2} -2*12 x^{3} y^{3}= \\ =12x*y^{2}*y^{3}+5*12*x* x^{3} *y^{2}-2*12x* x^{2} *y*y^{2}= \\ =12xy^{2}*y^{3}+12xy^{2}*5 x^{3} -12xy^{2}*2 x^{2} y= \\ =12xy^{2}(y^{3}+5 x^{3}-2 x^{2} y) [/tex]
The greatest common factor is thus [tex]12xy^{2}[/tex]
