Identify like terms in the following:

(a) – xy^{2}, – 4yx^{2}, 8x^{2}, 2xy^{2}, 7y, – 11x^{2}, – 100x, – 11yx, 20x2y, – 6x^{2}, y, 2xy, 3x

(b) 10pq, 7p, 8q, – p^{2}q^{2}, – 7qp, – 100q, – 23, 12q^{2}p^{2}, – 5p^{2}, 41, 2405p, 78qp, 13p^{2}q, qp^{2}, 701p^{2}

(a)

Expression | Variable Factors |

-xy | x, y, y |

-4yx | y, x, x |

8x | x, x |

2xy | x, y, y |

7y | y |

-11x | x, x |

-100x | x |

-11yx | y, x |

20x | x, x, y |

-6x | x, x |

y | y |

2xy | x, y |

3x | x |

So, From the above table we conclude that sets of like terms are

1. -xy^{2}, 2xy^{2} : As both have common variable factors as x, y and y

2. -4yx^{2}, 20x^{2}y : As both have common variable factors as x, x and y

3. 8x^{2} , -11x^{2}, -6x^{2} : As both have common variable factors as x and x

4. -11yx, 2xy : As both have common variable factors as x and y

5. -100x, 3x : As both have common variable factor as x

6. 7y, y : As both have common variable factor as y

(b)

Expression | Variable Factors |

100pq | p, q |

7p | P |

8q | q |

-p | p, p, q, q |

-7qp | q, p |

-100q | q |

-23 | Constant |

12q | q, q, p, p |

-5p | p, p |

41 | Constant |

2405p | p |

78qp | q, p |

13p | p, p, q |

qp | q, p, p |

701p | P, p |

So, From the above table we conclude that sets of like terms are

1. 10pq, –7qp, 78qp : As both have common variable factors as p and q

2. 7p, 2405p: As both have common variable factor as p

3. 8q, – 100q : As both have common variable factor as q

4. –p^{2}q^{2}, 12q^{2}p^{2} : As both have common variable factors as p, q, q and q

5. –23, 41 : As both terms are constant and don’t have any variable factor .

6. –5p^{2}, 701p^{2} :As both have common variable factors as p and p.

7. 13p^{2}q, qp^{2} : As both have common variable factors as p, p and q.

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