Question

Swami caught a bugler in this house true or false​

Answer 1

Explanation:

òlChanges made to your input should not affect the solution:

(1): "a3" was replaced by "a^3".

STEP

1

:

Equation at the end of step 1

(26•3a3) + 3

STEP

2

:

STEP

3

:

Pulling out like terms

3.1 Pull out like factors :

192a3 + 3 = 3 • (64a3 + 1)

Trying to factor as a Sum of Cubes:

3.2 Factoring: 64a3 + 1

Theory : A sum of two perfect cubes, a3 + b3 can be factored into :

(a+b) • (a2-ab+b2)

Proof : (a+b) • (a2-ab+b2) =

a3-a2b+ab2+ba2-b2a+b3 =

a3+(a2b-ba2)+(ab2-b2a)+b3=

a3+0+0+b3=

a3+b3

Check : 64 is the cube of 4

Check : 1 is the cube of 1

Check : a3 is the cube of a1

Factorization is :

(4a + 1) • (16a2 - 4a + 1)

Trying to factor by splitting the middle term

3.3 Factoring 16a2 - 4a + 1

The first term is, 16a2 its coefficient is 16 .

The middle term is, -4a its coefficient is -4 .

The last term, "the constant", is +1

Step-1 : Multiply the coefficient of the first term by the constant 16 • 1 = 16

Step-2 : Find two factors of 16 whose sum equals the coefficient of the middle term, which is -4 .

-16 + -1 = -17

-8 + -2 = -10

-4 + -4 = -8

-2 + -8 = -10

-1 + -16 = -17

1 + 16 = 17

2 + 8 = 10

4 + 4 = 8

8 + 2 = 10

16 + 1 = 17

Observation : No two such factors can be found !!