Algebraic Manupulation

$ab = 15 → 2ab = 30, -2ab = -30$

$→ a^2 + b^2 +2ab = (a+b)^2 = 40 + 30 = 70$

$a^2 + b^2 -2ab = (a-b)^2 = 40-30 = 10$

$→(a +b)^4 - (a-b)^4 = 70^2 -10^2$

$= (70 +10)(70-10) = 80\times60 =\boxed{4800}$

Given that,

• $a^2 +b^2 = 40$

• $ab = 15$

Now,

$(a+b)^4 - (a-b)^4$

$= \{(a+b)^2\}^2 - \{(a-b)^2\}^2$

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

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

$=\{40+2(15)\}^2 - \{40 - 2(15)\}^2$

$= (40 + 30)^2 - (40 - 30)^2$

$= (70)^2 - (10)^2$

$= \color{#20A900} \boxed{4800}$

BREAK THESE TYPE OF SUMS IN THE FORMULA

{a+b}{a+b}

ab=15

therefore

{a+b}{a+b}=40+{2 X 15}

{a-b}{a-b}=40-{2 X 15}