Explanation:
i).
(a + b)(5a – 3b) + (a – 3b)(a – b)
Expand each of the terms separately
That's
(a + b)(5a – 3b) = 5a² - 3ab + 5ab - 3b²
= 5a² + 2ab - 3b²
(a – 3b)(a – b) = a² - ab - 3ab + 3b²
= a² - 4ab + 3b²
Add the terms
That's
5a² + 2ab - 3b² + a² - 4ab + 3b²
Group like terms
5a² + a² + 2ab - 4ab - 3b² + 3b²
We have the answer as
6a² - 2ab
ii)
(a – b) (a² + b² + ab) – (a + b) (a² + b²– ab)
Expand the terms separately
For (a – b) (a² + b² + ab)
Using the rule
x³ - y³ = (x - y)( x² + xy + y²) expand the expression
So we have
(a – b) (a² + b² + ab) = a³ - b³
For (a + b) (a² + b²– ab)
Using the rule
x³ + y³ = (x + y)( x² - xy + y²) expand the expression
We have
(a + b) (a² + b²– ab) = a³ + b³
Subtract the terms
That's
a³ - b³ - (a³ + b³)
Remove the parenthesis
a³ - b³ - a³ - b³
Group like terms
a³ - a³ - b³ - b³
We have the final answer as
-2b³
iii)
(b² – 49) (b + 7) + 343
Expand the terms
That's
b³ + 7b² - 49b - 343 + 343
We have the final answer as
b³ + 7b² - 49b
Hope this helps you