Example 1: 9x

^{2}- 4y

^{2}

Solution:

Hence... | ||

Rewrite 9x^{2} - 4y^{2} as a difference of two squares: | 9x^{2} - 4y^{2} = (3x)^{2} - (2y)^{2} | |

Compare (3x)^{2} - (2y)^{2} with a^{2} - b^{2}: | a = 3x and b = 2y | |

Apply the formula a^{2}- b ^{2} = (a + b)(a - b): | (3x)^{2} - (2y)^{2} = (3x - 2y)(3x + 2y) |

Answer: (3x - 2y)(3x

+ 2y)

+ 2y)

Example 2: a

^{2}- 9b

^{2}

Solution:

Hence... | ||

Rewrite a^{2} - 9b^{2} as a difference of two squares: | a^{2} - 9b^{2} = a^{2} - (3b)^{2} | |

Compare a^{2} - (3b)^{2} with a ^{2} - b^{2}: | a = a and b = 3b | |

Apply the formula a^{2}- b ^{2} = (a + b)(a - b): | a^{2} - (3b)^{2} = (a + 3b)(a - 3b) |

Answer: (a + 3b)(a - 3b)

Example 3: 4x

^{2}- 25y

^{2}

Solution:

Hence... | ||

Rewrite 4x^{2} - 25y^{2} as a difference of two squares: | 4x^{2} - 25y^{2} = (2x)^{2} - (5y)^{2} | |

Compare (2x)^{2} - (5y)^{2} with a ^{2} - b^{2}: | a = 2x and b = 5y | |

Apply the formula a^{2}- b ^{2} = (a + b)(a - b): | (2x)^{2} - (5y)^{2} = (2x + 5y)(2x - 5y) |

Answer: (2x + 5y)(2x - 5y)

Example 4: x

^{2}- 1

Solution:

Hence... | ||

Rewrite x^{2} - 1 as a difference of two squares | x^{2} - 1^{2} | |

Compare x^{2} - 1^{2} with a^{2} - b^{2} | a= x and = 1b | |

Apply the formula a^{2} - b^{2} = (a + b)(a - b) | x^{2} - 1^{2} = (x + 1)(x - 1) |

Answer:

(x + 1)(x - 1)

(x + 1)(x - 1)

Example 5: 3x

^{2}- 3

Solution:

Hence... | ||

Take 3 as the common factor: | 3(x^{2} - 1) | |

Rewrite 3(x^{2} - 1) as a difference of two squares: | 3(x^{2} - 1^{2}) | |

Compare x^{2} - 1^{2} with : a^{2} - b^{2} | = x and a = 1b | |

Apply the formula : a^{2} - b^{2} = (a + b)(a - b) | 3(x^{2} - 1^{2}) = 3(x + 1)(x - 1) |

Answer:

3(x + 1)(x - 1)

3(x + 1)(x - 1)

Example 6: | x^2/4 - 1/4 |

Solution:

Hence... | ||||||

Rewrite the given expression as a difference of two squares: | ||||||

Compare: a^{2} - b^{2} | ||||||

Apply the formula : a^{2} - b^{2} = (a + b)(a - b) |

Answer:

**a**^{2}- b^{2}= (a + b)(a - b)
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