Question

6. Simplify: i) (a + b)(5a – 3b) + (a – 3b)(a – b) ii) (a – b) (a² + b² + ab) – (a + b) (a² + b²– ab) iii) (b² – 49) (b + 7) + 343

Answer 1

Step-by-step 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