Question

Evaluate: (-a)(b)(-a + b) if a= 6 and b= -3

Answer 1

There are two ways to solve this question.

1) To solve this question, we need to substitute a = 6 and b = -3 into the given expression and then evaluate:

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

= (-6)(-3)(-6 + (-3))

= 18(-9)

= -162

2) An alternative method is to simplify (-a)(b)(-a + b) into an expression without brackets and then substitute a = 6 and b = -3:

1. (-a)(b)(-a + b)

= (-ab)(-a + b)

= -ab*(-a) + (-ab)*b

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

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

2. a^(2)b - ab^(2)

= 6^(2)*(-3) - 6*(-3)^2

= 36*(-3) - 6*9

= -108 - 54

= -162

The key to either method is to be careful with placement of brackets, especially where there are negative values involved.