Answered

Join the conversation on IDNLearn.com and get the answers you seek from experts. Our platform offers reliable and detailed answers, ensuring you have the information you need.

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

What Is The GCF Of 1 14b2 35b2 2 18x3y2 42x2y3 3 12x2 16y2 4 3x2 9 You 12 5 45x3 60xy2 6 36x2 18x3 6 12x4 class=

Sagot :

[tex]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)[/tex]

[tex]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)[/tex]

[tex]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)[/tex]


[tex]GCF:\\1)\ b^2;\ 2)\ 6x^2y^2;\ 3)\ 4;\ 4);\ 3;\ 5);\ 15x;\ 6)\ 6x[/tex]
View image Аноним
Kate200468idn
[tex]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)[/tex]

[tex]Ans.\ GFC:\ 1)\ 7b^2,\ 2)\ 6x^2y^2,\ 3)\ 4,\ 4)\ 3,\ 5)\ 15x,\ 6)\ 6x[/tex]
We are happy to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. Thanks for visiting IDNLearn.com. We’re dedicated to providing clear answers, so visit us again for more helpful information.