Question

2a^2 - (-3a^2) + 4a^2 - (+5a^2) = ( )​

Answer 1

Answer:

The time period of a body executing S.H.M. is 0.05 s and the amplitude of vibration is 4

cm. What is the maximum velocity of the body

Answer 2

Answer

Final result :

4a2 • (a - 1) • (a - 3) • (2a + 1)

Step by step explanation

STEP

1

:

Equation at the end of step 1

((4•(a2))-4a)•(((2•(a3))-5a2)-3a)

STEP

2

:

Equation at the end of step

2

:

((4•(a2))-4a)•((2a3-5a2)-3a)

STEP

3

:

Equation at the end of step

3

:

(22a2 - 4a) • (2a3 - 5a2 - 3a)

STEP

4

:

STEP

5

:

Pulling out like terms

5.1 Pull out like factors :

4a2 - 4a = 4a • (a - 1)

STEP

6

:

Pulling out like terms

6.1 Pull out like factors :

(2a3 - 5a2 - 3a) = a • (2a2 - 5a - 3)

Trying to factor by splitting the middle term

6.2 Factoring 2a2 - 5a - 3

The first term is, 2a2 its coefficient is 2 .

The middle term is, -5a its coefficient is -5 .

The last term, "the constant", is -3

Step-1 : Multiply the coefficient of the first term by the constant 2 • -3 = -6

Step-2 : Find two factors of -6 whose sum equals the coefficient of the middle term, which is -5 .

-6 + 1 = -5 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -6 and 1

2a2 - 6a + 1a - 3

Step-4 : Add up the first 2 terms, pulling out like factors :

2a • (a-3)

Add up the last 2 terms, pulling out common factors :

1 • (a-3)

Step-5 : Add up the four terms of step 4 :

(2a+1) • (a-3)

Which is the desired factorization

Multiplying exponential expressions :

6.3 a1 multiplied by a1 = a(1 + 1) = a2