Q1 of 52 Page 131

Let’s resolve into factors:

6(a + b)2 + 5(a2-b2)-6(a-b)2


6(a + b)2 + 5(a2-b2)-6(a-b)2


=6(a + b)2 + 5(a-b)(a + b)-6(a-b)2


=6(a + b)2 + 9(a-b)(a + b)-4(a-b)(a + b)-6(a-b)2


=3(a + b){2a + 2b + 3a-3b}-2(a-b){2a + 2b + 3a-3b}


=3(a + b)(5a-b)-2(a-b)(5a-b)


=(5a-b)(3a + 3b-2a + 3b)


=(5a-b)(a + 5b)


∴ the factors of 6(a + b)2 + 5(a2-b2)-6(a-b)2 are (5a-b)(a + 5b)


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