Question

1. If ax3 – b3 = (3x – 2) (9x2 + 6x + 4), then the value
of a - (b)2 is
(1) 27
(2) 4
(3) 23
(4) 25​

Answer 1

Answer:

1 I think the filanent of this a perfec has a

Answer 2

Answer:

Option (3)

Step-by-step explanation:

Given:-

ax^3 – b^3 = (3x – 2) (9x^2 + 6x + 4)

To find:-

If ax^3 – b^3 = (3x – 2) (9x^2 + 6x + 4), then find the value of a - (b)^2

Solution:-

Given that :-

Method-1:-

ax^3 – b^3 = (3x – 2) (9x^2 + 6x + 4)

=>ax^3-b^3 = 3x(9x^2+6x+4)-2(9x^2+6x+4)

=>(3x×9x^2)+(3x×6x)+(3x×4)-(2×9x^2)-(2×6x)-(2×4)

=>ax^3-b^3 = 27x^3+18x^2+12x-18x^2-12x-8

=>ax^3-b^3 = 27x^3+(18x^2-18x^2)+(12x-12x)+(-8)

=>ax^3-b^3 = 27x^3+0+0-8

=>ax^3-b^3 = 27x^3 - 8

=>ax^3-b^3 = 27 x^3 - 2^3

On comparing both sides then

a = 27

b=2

(or)

Method -2:-

ax^3 – b^3 = (3x – 2) (9x^2 + 6x + 4)

=>ax^3-b^3 = (3x-2)[(3x)^2+(3x)(2)+(2)^2]

It is in the form of (a-b)(a^2+ab+b^2)

where a = 3x and b=2

We know that

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

=>ax^3 - b^3 = (3x)^3-(2)^3

=>ax^3 -b^3 = 27x^3-2^3

On comparing both sides then

a = 27

b=2

The value of a -b^2

=>27 - 2^2

=>27 - 4

=>23

The value is 23

Answer:-

The value of a - b^2 for the given problem is 23

Option (3)

Used formula:-

• a^3 - b^3= (a-b)(a^2+ab+b^2)