Question

Hi. ITS URGENT.
I need help with No 5 and 7 (see image)
Please show workings

Answer 1

I am just giving the expansion, so that you can substitute the values and solve it

Answer 2

5. a^3 + b^3 = (a+b)^3 - 3ab(a+b)

Explanation:

(a+b)^3

= (a+b) (a+b) (a+b)

={(a+b) (a+b)} (a+b)

={a(a+b) + b(a+b)} (a+b)

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

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

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

=a^3 + a^2b + ab^2 + b^3 + 2a^2b + 2ab^2

=a^3 + b^3 + 3a^2b + 3ab^2

=a^3 + b^3 + 3ab(a+b)

(a+b)^3 = a^3 + b^3 + 3ab(a+b)

(a+b)^3 - 3ab(a+b) = a^3 + b^3

a^3 + b^3 = (a+b)^3 - 3ab(a+b)

Hope this helped!