Question

(a) Find the L.C.M. of the expressions:

3a ^ 2 - 15a + 18 , 2a ^ 2 + 2a - 24 , 4a ^ 2 + 36a + 80

b) Find the G.C.D of the expressions:

24x ^ 3 * y ^ 4 * z ^ 2 , 18x ^ 2 * y ^ 3 * z ^ 3 , 36x ^ 4 * y ^ 2 * z ^ 4

​

Answer 1

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