2. Find the common factors of the following expressions. a. 6a² + 15a b. 20x³– 40x² + 80x c. 15x³y2 – 36x²y⁴+ 48xy³
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Answer:
(i)a
2
+8a+16
=a(a+4)+4(a+4)
=(a+4)(a+4)
(ii) p
2
−10p+25
=p(p−5)−5(p−5)
=(p−5)(p−5)
(iii) 25m
2
+30m+9
=5m(5m+3)+3(5m+3)
=(5m+3)(5m+3)
(iv) 49y
2
+84yz+36z
2
=49y
2
+42yz+42yz+36z
2
=7y(7y+6z)+6z(7y+6z)
=(7y+6z)(7y+6z)
(v) 4x
2
−8x+4
=(4x−4)(x−1)
=4(x−1)(x−1)
(vi) 121b
2
−88bc+16c
2
=(11b−4c)(11b−4c)
(vii) (l+m)
2
−4lm
=l
2
+m
2
+2lm−4lm
=l
2
+m
2
−2lm
=(l−m)(l−m)
(viii) a
4
+2a
2
b
2
+b
4
=(a
2
)
2
+2a
2
b
2
+(b
2
)
2
=[a
2
+b
2
]
2
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