Question

factorise then divide: 156y3(36y2-64)/104y2(6y+8)

Answer 1

Answer:

(12)(3y)( 6y − 8 )

Step-by-step explanation:

We have : 156 y3 ( 36y2 − 64 )104 y2 ( 6y + 8 )156 y3  36y2 - 64 104 y2  6y + 8  , So we write it , As :

⇒3y ( 36y2 − 64 )2 ( 6y + 8 )

⇒3y ( (6y)2 − 64 )2 ( 6y + 8 )

⇒3y ( ( 6y + 8 ) ( 6y − 8 ) )2 ( 6y + 8 )          ( As we know ( a2  − b2  ) = ( a − b )                          ( a  + b ) )

⇒3y  ( 6y + 8 ) ( 6y − 8 ) 2 ( 6y + 8 )

⇒3y  ( 6y − 8 ) 2

⇒(3y 2)( 6y − 8 )      

⇒(12)(3y)( 6y − 8 )

Answer 2

Answer:

((156•(y3))•——————————————)•y2)•(6y+8) 104

STEP2:

36y2 - 64 Simplify ————————— 104

STEP3:Pulling out like terms

 3.1     Pull out like factors :

   36y2 - 64  =   4 • (9y2 - 16) 

Trying to factor as a Difference of Squares:

 3.2      Factoring:  9y2 - 16 

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

         A2 - AB + BA - B2 =

         A2 - AB + AB - B2 =

         A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check :  9  is the square of  3 

Check : 16 is the square of 4

Check :  y2  is the square of  y1 

Factorization is :       (3y + 4)  •  (3y - 4) 

Equation at the end of step3:

(3y+4)•(3y-4) (((156•(y3))•—————————————)•y2)•(6y+8) 26

STEP 4 :

Equation at the end of step4:

(3y + 4) • (3y - 4) (((22•3•13y3) • ———————————————————) • y2) • (6y + 8) 26

STEP5:

Dividing exponents:

 5.1    22   divided by   21   = 2(2 - 1) = 21 = 2

Canceling Out:

 5.2      Canceling out  13  as it appears on both sides of the fraction line

Equation at the end of step5:

(6y3 • (3y + 4) • (3y - 4) • y2) • (6y + 8)

STEP6:

Multiplying exponential expressions :

 6.1    y3 multiplied by y2 = y(3 + 2) = y5

Equation at the end of step6:

(2•3y5) • (3y + 4) • (3y - 4) • (6y + 8)

STEP7:

STEP8:Pulling out like terms

 8.1     Pull out like factors :

   6y + 8  =   2 • (3y + 4) 

Multiplying exponents:

 8.2    21  multiplied by  21   = 2(1 + 1) = 22

Multiplying Exponential Expressions:

 8.3    Multiply  (3y + 4)  by  (3y + 4) 

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is  (3y+4)  and the exponents are :

          1 , as  (3y+4)  is the same number as  (3y+4)1 

 and   1 , as  (3y+4)  is the same number as  (3y+4)1 

The product is therefore,  (3y+4)(1+1) = (3y+4)2 

Final result :

(22•3y5) • (3y + 4)2 • (3y - 4)

Step-by-step explanation:

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