Question

(x+y)3 -(x-y)3 can be factorized as​

Answer 1

Answer:

(2x)(x²+y²)

Step-by-step explanation:

We know

a³ + b³ = (a + b)(a² – ab + b²)

so

(x+y)³ + (x-y)³ = ((x+y) + (x-y))((x+y)² – (x+y)(x-y) + (x-y)²)

(x+y)³ + (x-y)³ = (2x)(x²+2xy+y² - x²-y²+x²-2xy+y²)

 [use  the identities (a+b)²=a²+2ab+b²,   (a+b)(a-b)= a²-b²]

(x+y)³ + (x-y)³ = (2x)(x²+y²)

hope it helps

Answer 2

Answer:

(2x)(x ^ 2 + y ^ 2)

Step-by-step explanation:

We know

a ^ 3 + b ^ 3 = (a + b)(a ^ 2 - ab + b ^ 2)

SO

(x+y)³ + (x-y)³ = ((x+y) + (x−y))((x+y)² − (x+y) - (x-y)+(x-y)^ 2 )

(x+y)³ + (x-y)³ = (2x)(x²+2xy+y² x^ 2 -y^ 2 +x^ 2 -2xy+y^ 2 )

[use the identities (a + b) ^ 2 = a ^ 2 + 2ab + b ^ 2 , (a+b)(a-b)=a^ 2 -b^ 2 ]

(x + y) ^ 3 + (x - y) ^ 3 = (2x)(x ^ 2 + y ^ 2)

hope it helps

Step-by-step explanation:

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