2<\/sup> – 20y – 8z + 2yz
\n= 5y x y – 4 x 5y – 2 x 2 x 2 x z + 2 x y x z
\n= 5y (y – 4) + 2z (- 4 + y)
\n= 5y (y – 4) + 2z (y – 4)
\n= (y – 4) (5y + 2z)<\/p>\n(viii) 10ab + 4a + 5b + 2
\n= 2 x 5 x a x b + 2 x 2 x a + 5 x b + 2
\n= 2a (5b + 2) + 1 (5b + 2)
\n= (5b + 2) (2a + 1)<\/p>\n
<\/p>\n
(ix) 6xy – 4y + 6 – 9x
\n= 2 x 3 x x x y – 2 x 2 x y + 2 x 3 – 3 x 3 x x
\n= 2y (3x – 2) + 3 (2 – 3x)
\n= 2y (3x – 2) – 3 (3x – 2)
\n= (3x – 2) (2y – 3)<\/p>\n
Question 4.
\nFactorise
\n(i) a4<\/sup> – b4<\/sup>
\n(ii) p4<\/sup> – 81
\n(iii) x4<\/sup> – (y + z)4<\/sup>
\n(iv) x24<\/sup> – (x – z)
\n(v) a4<\/sup> – 2a2<\/sup>b2<\/sup> + b4<\/sup>
\nAnswer:
\n(i) a4<\/sup> – b4<\/sup>
\n= (a2<\/sup>)2<\/sup> – (b2<\/sup>)2<\/sup>
\n[(using a2<\/sup> – b2<\/sup> = (a + b) (a – b)]
\n= (a2<\/sup> + b2<\/sup>) (a2<\/sup> – b2<\/sup>)
\n= (a2<\/sup> + b2<\/sup>) (a + b) (a – b)<\/p>\n(ii) p4<\/sup> – 81
\n= (p2<\/sup>)2<\/sup> – 92<\/sup>
\n[Using a2<\/sup> – b2<\/sup> = (a + b) (a – b)]
\n= (p2<\/sup> + 9) (p2<\/sup> – 9)
\n= (P2<\/sup> + 9) [p2<\/sup> – 32 ]
\n= (p2<\/sup> + 9) (p + 3) (p – 3)<\/p>\n(iii) x2<\/sup> – (y + z)4
\n= (x2<\/sup>)2<\/sup> – [(y + z)2<\/sup>]2<\/sup>
\n[using a2<\/sup> – b2<\/sup> = (a + b) (a – b)
\n= [x2<\/sup> + (y + z)2<\/sup>] [x2<\/sup> – (y + z)2<\/sup>]
\n= [x2<\/sup> + (y + z2<\/sup>)] (x + y + z) [x – (y + z)
\n= [x2<\/sup> + (y + z)2<\/sup>] [x + y + z) (x – y – z)<\/p>\n(iv) x4<\/sup> – (x – z)4<\/sup>
\n= (x2<\/sup>)2<\/sup> – [(x-z)2<\/sup>]2<\/sup>
\n= [x2<\/sup> + (x – z)2<\/sup>] [x2<\/sup> – (x – z)2<\/sup>]