Question
Mathematics Question on What is Factorisation?
Factorise the following expressions.
- a2+8a+16
- p2−10p+25
- 25m2+30m+9
- 49y2+84yz+36z2
- 4x2−8x+4
- 121b2−88bc+16c2
- (l+m)2−4lm (Hint: Expand (l+m)2 first)
- a4+2a2b2+b4
Answer
(i) a2+8a+16=(a)2+2×a×4+(4)2
=(a+4)2[(x+y)2=x2+2xy+y2]
(ii) p2−10p+25=(p)2−2×p×5+(5)2
= (p−5)2[(a−b)2=a2−2ab+b2]
(iii) 25m2+30m+9=(5m)2+2×5m×3+(3)2
= (5m+3)2[(a+b)2=a2+2ab+b2]
(iv) 49y2+84yz+36z2=(7y)2+2×(7y)×(6z)+(6z)2
= (7y+6z)2[(a+b)2=a2+2ab+b2]
(v) 4x2−8x+4=(2x)2−2(2x)(2)+(2)2
= (2x−2)2[(a−b)2=a2−2ab+b2]
= [(2)(x−1)]2=4(x−1)2
(vi) 121b2−88bc+16c2=(11b)2−2(11b)(4c)+(4c)2
= (11b−4c)2[(a−b)2=a2−2ab+b2]
(vii) (l+m)2−4lm=l2+2lm+m2−4lm
=l2−2lm+m2
= (l−m)2[(a−b)2=a2−2ab+b2]
(viii) a4+2a2b2+b4=(a2)2+2(a2)(b2)+(b2)2
= (a2+b2)2[(a+b)2=a2+2ab+b2]