Factorise x²+4a+4x+ax​

Step-by-step explanation:

STEP

1

:

Equation at the end of step 1

 ((a • (x4)) -  5ax2) +  4a

STEP

2

:

STEP

3

:

Pulling out like terms

3.1     Pull out like factors :

  ax4 - 5ax2 + 4a  =   a • (x4 - 5x2 + 4)  

Trying to factor by splitting the middle term

3.2     Factoring  x4 - 5x2 + 4  

The first term is,  x4  its coefficient is  1 .

The middle term is,  -5x2  its coefficient is  -5 .

The last term, "the constant", is  +4  

Step-1 : Multiply the coefficient of the first term by the constant   1 • 4 = 4  

Step-2 : Find two factors of  4  whose sum equals the coefficient of the middle term, which is   -5 .

     -4    +    -1    =    -5    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -4  and  -1  

                    x4 - 4x2 - 1x2 - 4

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

                   x2 • (x2-4)

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

                    1 • (x2-4)

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

                   (x2-1)  •  (x2-4)

            Which is the desired factorization

Trying to factor as a Difference of Squares:

3.3      Factoring:  x2-1  

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 : 1 is the square of 1

Check :  x2  is the square of  x1  

Factorization is :       (x + 1)  •  (x - 1)  

Trying to factor as a Difference of Squares:

3.4      Factoring:  x2 - 4  

Check : 4 is the square of 2

Check :  x2  is the square of  x1  

Factorization is :       (x + 2)  •  (x - 2)  

Final result :

 a•(x+1)•(x-1)•(x+2)•(x-2)

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answer: idk wbu

step-by-step explanation: