Question 5:
(a) Simplify:
(m – 4n)(m + 4n) – m2
(b) Simplify:
3x−3yx+y×2x+2y6x3x−3yx+y×2x+2y6x
Solution:
(a)
(m – 4n)(m + 4n) – m2
= m2 + 4mn – 4mn – 4n2 – m2
= 0
(b)
3x−3yx+y×2x+2y6x=3(x−y)x+y×2(x+y)6x=x−yx
Question 6:
(a) Simplify each of the following:
(a) Simplify each of the following:
(i)12mn32(ii)x2−xyx
(b) Express 12q−2p−76q as a single fraction in its simplest form.
(b) Express 12q−2p−76q as a single fraction in its simplest form.
Solution:
(a)(i)12mn32=3mn8(a)(ii)x2−xyx=x(x−y)x=x−y
(b)
12q−2p−76q=1×32q×3−(2p−7)6q=3−2p+76q=10−2p6q=2(5−p)36q=5−p3q
Question 7:
(a) Factorise 2ae + 3af – 6de – 9df
(b) Simplify
a2−b2(a+b)2
Solution:
(a)
2ae + 3af – 6de – 9df = a (2e + 3f ) – 3d (2e + 3f)
= (2e + 3f ) (a – 3d)
(b)
a2−b2(a+b)2=(a+b)(a−b)(a+b)(a+b)=a−ba+b
Question 8:
(a) Factorise –8c2 – 12ac.
(b) Simplify
ae+ad−2be−2bda2−4b2.
Solution:
(a)
–8c2– 12ac
= –4c (2c + 3a)
(b)
ae+ad−2be−2bda2−4b2=a(e+d)−2b(e+d)(a+2b)(a−2b)=(e+d)(a−2b)(a+2b)(a−2b)=e+da+2b
