Question

simplify :- (2x-5y)³+(2x+5y)³​

Answer 1

✠EXPLANATION:-

✠ Given to simplify:-

(2x-5y)³+(2x+5y)³

✠ Answer :-

16x³ + 300xy²

✠Solution:-

As we know that ,

⟶ (a+b)³ = a³+ b³ + 3ab(a+b)

⟶ (a-b)³ = a³ -b³ -3ab(a-b)

So, by using these formulae we can expand the following and can simplify it

⟶ (2x +5y)³ +(2x-5y)³

⟶ (2x)³ + (5y)³ +3(2x)(5y)[2x+5y] + (2x)³ -(5y)³ -3(2x)(5y) [2x-5y]

⟶ 8x³ + 125y³ + 30xy[2x+5y] + 8x³ - 125y³ - 30xy[2x-5y]

⟶ 8x³ +125y³ + 60x²y + 150xy²+ 8x³ - 125y³ - 60x²y + 150xy²

✠Keep like terms together

⟶ 8x³ + 8x³ +60x²y -60x²y + 150xy² + 150xy² + 125y³ - 125y³

⟶ 16x³ + 300xy²

So, the value of (2x-5y)³+(2x+5y)³ is 16x³ + 300x

✠Know more :-

⟶(a+ b)² = a² + b² + 2ab

⟶( a - b )² = a² + b² - 2ab

⟶( a + b )² + ( a - b)² = 2a² + 2b²

⟶( a + b )² - ( a - b)² = 4ab

⟶( a + b + c )² = a² + b² + c² + 2ab + 2bc + 2ca

⟶a² + b² = ( a + b)² - 2ab

⟶(a+b)(a-b) = a²-b²

⟶ If a + b + c = 0 then a³ + b³ + c³ = 3abc

Answer 2

This is your answer. Hope it will help you a lot.