MATHS......

1.Evaluate 1^a+(a+1)^0 ÷2^ -3 where a not equal to-1
[1^a+(a+1)^0]/2^-3
= 8(1^a+1)
8(1^a+1)not = -1
1^a +1 not = -1/8
1^a not = -9/8
a not = log (-9/8)/log1, which is undefined.
2.Factorize a^2-4b^2
a^2-4b^2 = a^2-(2b)^2
= (a-2b)(a+2b)
3.Factorize4/3 K^2 -3
4/3 k^2 - 3
= 3(4/9 k^2 -1)
=3[(2/3 k)^2 -1^2]
= 2(2k/3 -1)(2k/3 +1)
4.Factorize25-(a-3)^2
25-(a-3)^2
= 5^2 -(a-3)^2
= (5-a+3)(5+a-3)
= (8-a)(2+a)
5.Factorize(a+2b)^2-(2a-b)^2
(a+2b)^2-(2a-b)^2
= (a+2b-2a+b)(a+2b+2a-b)
= (-a+3b)(3a-b)
6.Factorize x^2-4y^2-2x+4y
x^2-4y^2-2x+4y
= x^2 -(2y)^2 -2(x+2y)
= (x-2y)(x+2y)-2(x+2y)
= (x-2y-2)(x+2y)
7.Factorize 3x^3-24
3x^3-24
= 3(x^3 - 2^3)
= 3(x-2)(x^2 + 2x + 4)
8.Factorize a^3+8b^6
a^3+8b^6
= a^3 + (2b^2)^3
= (a+2b^2)(a^2 - 2ab^2 + 4b^4)
9.Factorize x^2-16
x^2-16
= x^2 -4^2
= (x-4)(x+4)
10a Factorize a^2+4a+4
a^2+4a+4
= a^2 + 2*2*a+2^2
= (a+2)^2
b.Factorize b^2-6b+9
b^2 - 6b + 9
= b^2 - 2*3*b +3^2
= (b-3)^2
c.Using the results of (a) and (b), factorize a^2+4a- b^2+6b-5
a^2+4a- b^2+6b-5
= a^2+4a- b^2+6b+(4-9)
= (a^2+4a+4)- (b^2-6b+9)
= (a+2)^2 - (b-3)^2
= (a+2-b+3)(a+2+b-3)
= (a-b+5)(a+b-1)