Question

1. Factorise the following expressions.
(1) a² + 8a + 16 (i) p2 - 10 p + 25 (ii) 25m2 + 30m + 9
(iv) 49y2 + 84yz + 3622
(v) 4x2 - 8x + 4
(vi) 121b2-88bc + 16c2
(vii) (1 + m)- 41m (Hint: Expand (1 + m)2 first)
( af + 2a-b2 + b4​

Answer 1

Answer:

1)a²+8a+16

=a²+4a+4a+16

=(a²+4a)+(4a+16)

=a(a+4)+4(a+4)

=(a+4)(a+4)

=(a+4)²

2)p²-10p+25

=p²-5p-5p+25

=(p²-5p)-(5p+25)

=p(p-5)-5(p-5)

=(p-5)(p-5)

=(p-5)²

3)25m²+30m+9

=25m²+15m+15m+9

=(25m²+15m)+(15m+9)

=5m(5m+3)+3(5m+3)

=(5m+3)(5m+3)

=(5m+3)²

4)49y²+84yz+36z²

=(7y)²+2(7y)(6z)+(6z)²

=(7y+6z)²

5)4x²-8x+4

=x²-2x+1

=x²-x-x+1

=(x²-x)-(x+1)

=x(x-1)-1(x-1)

=(x-1)(x-1)

=(x-1)²

6)121b²-88bc+16c²

=(11b)²-2(11b)(4c)+(4c)²

=(11b+4c)²

7)(1+m)²-41m

=1+2m+m²-41m

=m²+2m-41m+1

=m²-39m+1

I'm not sure about the 7th question