a Expand the expression b Simplify the expression c Simplify

(a) Expand the expression: (b) Simplify the expression: (c) Simplify the expression: (x - 3)(2x + 7) = 2x^2 + x - 21 5 squareroot -32 = -2 a^2 - b^2/a^2 - 2ab + b^2 = a + b/a - b: a notequalto b

Solution

a) ( x- 3) ( 2x + 7 )

using foil method to expand the expression

2x^2 + 7x - 6x - 21

2x^2 + x - 21

b) 5th root ( -32 )

-32 can be written in its factors

-32 = -2^ 5

5th root means raised to power 1/5

hence, we can write

(-2^5 )^1/5

= -2

c) ( a^2 - b^2 ) / ( a^2 - 2ab + b^2 )

factoring top and bottom expressions

a^2 - b^2 = (a-b) (a+b)

a^2 - 2a + b^2 = (a-b)^2

now the expression becomes

( a-b) (a+b) / (a-b) (a-b)

= a+b / a-b

a should not be equal to b