Algebra MATHS questions

1)Which real numbers are equal to their
cubes?
0 , 1 , -1 are all equal to their respective cubes.
2)Write 4×10-2 as a decimal.
0.04
3)Write 0.12×10-3 as a decimal.
0.00012
4)Write 2 log3 x + log3 5 as a single logarithmic
expression.
= log3 x2 + log 35 = log3(5x2)
5)Factor the algebraic expression 6x2-
21xy+8xz-28yz.
= 3x(2x - 7y) + 4z(2x - 7y) = (2x - 7y)(3x + 4z)
6)Factor the algebraic expression (x - 1)2-(y-
2)2.
= [(x - 1)- (y - 2)][(x - 1)+ (y - 2)] = (x - y + 1)(x + y - 3)
7)Factor the algebraic expression x2 – z4.
= (x + z2)(x – z2) = (x + z2)(x + z)(x - z)

, 8)Evaluate the algebraic expression |-2 x - y +
3| for x = 3 and y = 5
= |-2(3) - (5) + 3| = |-8| = 8
9)Simplify the algebraic expression -2(x - 3) +
4(-2 x + 8)
= -2x + 6 -8x + 32 = -10x + 38
10)Expand and simplify the algebraic
expression (x + 3)(x - 3) - (-x - 9)
= x2 - 9 + x + 9 = x 2 + x
11)Which property is used to write a(x + y) = a
x+ay
distributivity
12)Simplify (8x3)/(2x-3)
4 x6
13)Simplify (-a2b3)2(c2)0
a 4b6


14)For what value of k is the point (-2, k) on
the line with equation -3x+3y = 4?