Question

What is the GCF of

1.) 14b^2 - 35b^2
2.) 18x^3y^2 + 42x^2y^3
3.) 12x^2 + 16y^2
4.) 3x^2 - 9 you + 12
5.) 45x^3 - 60xy^2
6.) 36x^2 + 18x^3 - 6 + 12x^4

Answer 1

`1.) 14b^2 - 35b^3=2\cdot7b^2-5b\cdot7b^2=7b^2(2-5b)\\\\2.) 18x^3y^2 + 42x^2y^3=3x\cdot6x^2y^2+7y\cdot6x^2y^2=6x^2y^2(3x+7y)\\\\3.) 12x^2 + 16y^2=4(3x^2+4y^2)\\\\4.) 3x^2 - 9xy + 12y=3(x^2-3xy+4)\\\\5.) 45x^3 - 60xy^2=3x^2\cdot15x-4y^2\cdot15x=15x(3x^2-4y^2)\\\\6.)36x^2+18x^3-6x+12x^4=6x(2x^3+3x^2+6x-1)`


`Ans.\ GFC:\ 1)\ 7b^2,\ 2)\ 6x^2y^2,\ 3)\ 4,\ 4)\ 3,\ 5)\ 15x,\ 6)\ 6x`

Answer 2

`1.\\14b^2-35b^3\\GCF(14;35)=7\\GCF(b^2;b^3)=b^2\\14b^2-35b^3=7b^2(2-5b)\\\\2.\\18x^3y^2+42x^2y^3\\GCF(18;42)=6\\GCF(x^3y^2;x^2y^3)=x^2y^2\\18x^3y^2+42x^2y^3=6x^2y^2(3x+7y)`


`3.\\12x^2+16y^2\\GCF(12;16)=4\\GCF(x^2;y^2)=1\\12x^2+16y^2=4(3x^2+4y^2)\\\\4.\\3x^2-9xy+12y\\GCF(3;9;12)=3\\GCF(x^2;xy;y)=1\\3x^2-9xy+12y=3(x^2-3xy+4y)`


`5.\\45x^3-60xy^2\\GCF(45;60)=15\\GCF(x^3;xy^2)=x\\45x^3-60xy^2=15x(3x^2-4y^2)\\\\6.\\36x^2+18x^3-6x+12x^4\\GCF(36;18;6;12)=6\\GCF(x^2;x^3;x;x^4)=x\\36x^2+18x^3-6x+12x^4=6x(6x+3x^2-1+2x^3)`



`GCF:\\1)\ b^2;\ 2)\ 6x^2y^2;\ 3)\ 4;\ 4);\ 3;\ 5);\ 15x;\ 6)\ 6x`