1. Factorise the following.
a.
4x2 + 4x+ 1
d. 9m2 + 24m + 16
b2 + 14b + 49
1
1. 36x² + 6s +
4
b. 9y2 + 12yz + 4z2
e. 4t2 + 20t + 25
h. 36n2 + 36n + 9
C. 16p2 + 40p + 25
f. a2 + 8a + 16
i. 1 + 18k + 81k2
2.
Factorise the following
a x² - 6x + 9
d. 16d2 - 24d + 9
g. 12162 - 22b + 1
j. p²q² - 2pq + 1
b. a? - 10a + 25
1 - 4m + m2
h. 36 - 12k + k2
e.
c. 9p2 - 12p + 4
f. 81y2 - 36y + 4
1
i.
3n + 9n2
4
11 -
Answers
Answer:
Q)4x²+4x+1
=4x²+2x+2x+1
=(4x²+2x)+(2x+1)
=2x(2x+1)+1(2x+1)
=(2x+1)(2x+1)
=(2x+1)²
Q)9m²+24m+16
=9m²+12m+12m+16
=(9m²+12m)+(12m+16)
=3m(3m+4)+4(3m+4)
=(3m+4)(3m+4)
=(3m+4)²
Q)b²+14b+49
=b²+7b+7b+49
=(b²+7b)+(7b+49)
=b(b+7)+7(b+7)
=(b+7)(b+7)
=(b+7)²
Q)9y²+12yz+4z²
=9y²+6yz+6yz+4z²
=(9y²+6yz)+(6yz+4z²)
=3y(3y+2z)+2z(3y+2z)
=(3y+2z)(3y+2z)
=(3y+2z)²
Q)4t²+20t+25
=4t²+10t+10t+25
=(4t²+10t)+(10t+25)
=2t(2t+5)+5(2t+5)
=(2t+5)(2t+5)
=(2t+5)²
Q)36n²+36n+ 9
=4n²+4n+1
=4n²+2n+2n+1
=(4n²+2n)+(2n+1)
=2n(2n+1)+1(2n+1)
=(2n+1)(2n+1)
=(2n+1)²
Q)16p²+40p+25
=16p²+20p+20p+25
=(16p²+20p)+(20p+25)
=4p(4p+5)+5(4p+5)
=(4p+5)(4p+5)
=(4p+5)²
Q)a²+8a+16
=a²+4a+4a+16
=(a²+4a)+(4a+16)
=a(a+4)+4(a+4)
=(a+4)(a+4)
=(a+4)²
Q)1+18k+81k²
=81k²+18k+1
=81k²+9k+9k+1
=(81k²+9k)+(9k+1)
=9k(9k+1)+1(9k+1)
=(9k+1)(9k+1)
=(9k+1)²
Q)x²-6x+9
=x²-3x-3x+9
=(x²-3x)-(3x+9)
=x(x-3)-3(x-3)
=(x-3)(x-3)
=(x-3)²
Q)16d²-24d+9
=16d²-12d-12d+9
=(16d²-12d)-(12d+9)
=4d(4d-3)-3(4d-3)
=(4d-3)(4d-3)
=(4d-3)²
Q)a²-10a+25
=a²-5a-5a+25
=(a²-5a)-(5a+25)
=a(a-5)-5(a-5)
=(a-5)(a-5)
=(a-5)²
Q)36-12k+k²
=k²-12k+36
=k²-6k-6k+36
=(k²-6k)-(6k+36)
=k(k-6)-6(k-6)
=(k-6)(k-6)
=(k-6)²
Q)9p²-12p+4
=9p²-6p-6p+4
=(9p²-6p)-(6p+4)
=3p(3p-2)-2(3p-2)
=(3p-2)(3p-2)
=(3p-2)²