Math, asked by kengealka01, 2 months ago

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

Answers

Answered by vkamble0104
0

Answer:

1 answer is

Step-by-step explanation:

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Answered by junaida8080
0

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}.

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