Factor the expression using the two different techniques listed for Parts 1(a) and 1(b).

SamJones
Feb 24, 2018

#1**+1 **

a) In order to factor using this method, let's try and identify the GCF first. 9 is the greatest common factor between 36 and 81. a^4 is the greatest common factor between the a's, and b^10 is the factor for the b's. Let's factor it out!

\(36a^4b^{10}-81a^{16}b^{20}\) | Factor out the GCF, \(9a^4b^{10}\), like I described earlier. |

\(9a^4b^{10}\left(4-9a^{12}b^{10}\right)\) | Don't stop here, though! Notice that the resulting binomial is a difference of squares. |

\(9a^4b^{10}\left(2+3a^6b^5\right)\left(2-3a^6b^5\right)\) | |

b) The beginning binomial is a difference of squares to begin with, so it is possible to start with this first!

\(36a^4b^{10}-81a^{16}b^{20}\) | Let's do this approach this time! |

\(\left(6a^2b^5+9a^8b^{10}\right)\left(6a^2b^5-9a^8b^{10}\right)\) | Don't stop yet! Both binomials have their own GCF's! |

\(3a^2b^5\left(2+3a^6b^5\right)*3a^2b^5\left(2-3a^6b^5\right)\) | Combine the multiplication. |

\(9a^4b^{10}\left(2+3a^6b^5\right)\left(2-3a^6b^5\right)\) | |

Well, these are the two techniques.

TheXSquaredFactor
Feb 24, 2018

#1**+1 **

Best Answer

a) In order to factor using this method, let's try and identify the GCF first. 9 is the greatest common factor between 36 and 81. a^4 is the greatest common factor between the a's, and b^10 is the factor for the b's. Let's factor it out!

\(36a^4b^{10}-81a^{16}b^{20}\) | Factor out the GCF, \(9a^4b^{10}\), like I described earlier. |

\(9a^4b^{10}\left(4-9a^{12}b^{10}\right)\) | Don't stop here, though! Notice that the resulting binomial is a difference of squares. |

\(9a^4b^{10}\left(2+3a^6b^5\right)\left(2-3a^6b^5\right)\) | |

b) The beginning binomial is a difference of squares to begin with, so it is possible to start with this first!

\(36a^4b^{10}-81a^{16}b^{20}\) | Let's do this approach this time! |

\(\left(6a^2b^5+9a^8b^{10}\right)\left(6a^2b^5-9a^8b^{10}\right)\) | Don't stop yet! Both binomials have their own GCF's! |

\(3a^2b^5\left(2+3a^6b^5\right)*3a^2b^5\left(2-3a^6b^5\right)\) | Combine the multiplication. |

\(9a^4b^{10}\left(2+3a^6b^5\right)\left(2-3a^6b^5\right)\) | |

Well, these are the two techniques.

TheXSquaredFactor
Feb 24, 2018