Question

5a+3b whole cube - 5a-3b whole cube

Answer 1

Answer:

(5a+3b)³ - (5a-3b)³

= (5a)³+3*(5a)²*3b+3*5a*(3b)²+(3b)³- [(5a)³-3*(5a)²*3b+3*5a*(3b)²-(3b)³]

=(5a)³+3*(5a)²*3b+3*5a*(3b)²+(3b)³-(5a)³+3*(5a)²*3b-3*5a*(3b)²+(3b)³

=2*3*(5a)²*3b+2*(3b)³

=450a²b+54b³

Hope this helps you :)

Answer 2

The solution for this question is

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

(5a+3b)^3 = 125a^3+27b^3+45ab (5a+3b)

= 125a^3+27b^3+225a^2b +135ab^2

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

(5a-3b)^3 = 125a^3-27b^3-45ab (5a-3b)

= 125a^3-27b^3-225a^2b+135ab^2

now as per the equation

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

=(125a^3+27b^3+225a^2b+135ab^2) - (125a^3-27b^3-225a^2b+135ab^2)

now opening the brackets,

=125a^3+27b^3+225a^2b+135ab^2-125a^3+27b^3+225a^2b-135ab^2

positive and negative sign, similar terms get cancelled,

Now left out are:

=27b^3+27b3+225a^2b+225a^2b

the answer is

=54b^3+450a^2b

or

=b (54b^2 + 450a^2)