Question

Simplify the following
(5x + 2y)^3 - (5x – 2y)^3​

Answer 1

Step-by-step explanation:

$(5x + 2y)^3 - (5x – 2y)^3 \\ = (5x + 2y - 5x + 2y)[ ( {5x + 2y)}^{2} + (5x + 2y)(5 x - 2y) + (5x - 2y) {}^{2} ] \\ = 4y[ ( {5x})^{2} + (2 {y})^{2} +( 2.5x.2y) + (5 {x})^{2} - (2 {y})^{2} + ( {5x})^{2} + (2 {y})^{2} - ( 2.5x.2y) ] \\ = 4y[ 25 {x}^{2} + 4 {y}^{2} + 20xy + 25 {x}^{2} - 4 {y}^{2} + 25 {x}^{2} + 4 {y}^{2} - 20xy ] \\ = 4y(75 {x}^{2} + 4 {y}^{2} )$

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Answer 2

Answer:

✡16y³+300x²y☑

Step-by-step explanation:

${(5x + 2y)}^{3} - {(5x - 2y)}^{3}$

⚫Using identity:-

✡ (a+b) ³= a³+b³+3ab(a+b) and

✡(a-b) ³= a³-b³-3ab(a-b)

➡[(5x)³+(2y)³+3×5x×2y(5x+2y)]-[(5x)³-(2y)³-3×5x×2y(5x-2y)]

➡[125x³+8y³+30xy(5x+2y)]-[125x³-8y³-30xy(5x-2y)]

➡[125x³+8y³+150x²y+60xy²]-[125x³-8y³-150x²y+60xy²]

➡125x²+8y³+150x²y+60xy²-125x³+8y³+150x²y-60xy²

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

➡16y³+300x²y

Hope this is helpful to you!