Question

please give me answer this question this is very urgent​

Answer 1

Step-by-step explanation:

Solutions:-

(i) Given expression is (2x+1)^3

It is in the form of (a+b)^3

Where , a= 2x and b =1

We know that

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

On Substituting these values then

=> (2x)^3 +3(2x)^2(1)+3(2x)(1)^2+(1)^3

=> 8x^3 + 3(4x^2)+6x(1)+1

=>8x^3+12x^2+6x+1

(2x+1)^3 = 8x^3+12x^2+6x+1

_________________________________

ii).Given expression is (2a-3b)^3

It is in the form of (a-b)^3

Where , a= 2a and b =3b

We know that

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

On Substituting these values then

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

=> 8a^3 -3(4a^2)(3b)+3(2a)(9b^2)+27b^3

=>8a^3-36a^2b+54ab^2+27b^3

(2a-3b)^3 = 8a^3-36a^2b+54ab^2+27b^3

___________________________________

iii)Given expression is (3/2 x+ 1)^3

It is in the form of (a+b)^3

Where , a= 3x/2 and b =1

We know that

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

On Substituting these values then

=> (3x/2)^3+3(3x/2)^2(1)+3(3x/2)(1)^2+(1)^3

=> 27x^3/8 +3(9x^2/4)+(9x/2)+1

=>(27/8)x^3 +(27/4)x^2+(9/2)x+1

(3/2 x+ 1)^3 = (27/8)x^3 +(27/4)x^2+(9/2)x+1

____________________________________

iv)Given expression is (x-(2y/3))^3

It is in the form of (a-b)^3

Where , a= x and b =2y/3

We know that

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

On Substituting these values then

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

=>x^3 -2x^2 y+(4xy^2/3)-(8y^3/27)

=>x^3 -2x^2y+(4/3)xy^2-(8/27)y^3

(x-(2y/3))^3 = x^3 -2x^2y+(4/3)xy^2-(8/27)y^3

_____________________________________

Used formulae:-

• (a+b)^3=a^3+3a^2b+3ab^2+b^3

• (a-b)^3=a^3-3a^2b+3ab^2-b^3