Question

(1) (3x + y)³ - (3x - y)³
(2) (2x - 5y)³ + (2x + 5y)³​

Answer 1

Answer:

1 answer is

Step-by-step explanation:

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Answer 2

Answer:

$(3x+y)^{3}-(3x-y)^{3}=2y^{3}+54x^{2}y$

$(2x-5y)^{3}+(2x+5y)^{3}=16x^{3}+300xy^{2}$

Step-by-step explanation:

Given equations are

$(3x+y)^{3}-(3x-y)^{3}$,

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

Use the formulae:

$(a+b)^{3}=a^{3}+b^{3}+3a^{2}b+3ab^{2}\\(a-b)^{3}=a^{3}-b^{3}-3a^{2}b+3ab^{2}$

In the first equation, we have

$a=3x$, $b=y$.

In this problem, we find the values of $(3x+y)^{3}$, $(3x-y)^{3}$ and subtract them.

Finding the value of $(3x+y)^{3}$,

$(3x+y)^{3}=(3x)^{3}+y^{3}+3(3x)^{2}y+3(3x)(y)^{2}$

$=27x^{3}+y^{3}+27x^{2}y+9xy^{2}$

Now finding the value of $(3x-y)^{3}$,

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

$=27x^{3}-y^{3}-27x^{2}y+9xy^{2}$

Now subtracting the two values, we get

$(3x+y)^{3}-(3x-y)^{3}=27x^{3}+y^{3}+27x^{2}y+9xy^{2}-(27x^{3}-y^{3}-27x^{2}y+9xy^{2})$

$=27x^{3}+y^{3}+27x^{2}y+9xy^{2}-27x^{3}+y^{3}+27x^{2}y-9xy^{2}$

$=2y^{3}+54x^{2}y$.

So the value after subtraction is $2y^{3}+54x^{2}y$.

In the second equation, we have

$a=2x$, $b=5y$.

In this problem, we find the values of $(2x-5y)^{3},(2x+5y)^{3}$ and add them.

Finding the value of $(2x-5y)^{3}$,

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

$=8x^{3}-125y^{3}-60x^{2}y+150xy^{2}$

Now finding the value of $(2x+5y)^{3}$,

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

$=8x^{3}+125y^{3}+60x^{2}y+150xy^{2}$

Now adding the two values, we get

$(2x-5y)^{3}+(2x+5y)^{3}=8x^{3}-125y^{3}-60x^{2}y+150xy^{2}+8x^{3}+125y^{3}+60x^{2}y+150xy^{2}$

$=16x^{3}+300xy^{2}$

So the value after addition is $16x^{3}+300xy^{2}$.