Question

(4x-9)(2x^2+2x+1) (4x−9)(2x 2 +2x+1)

Answer 1

Answer:

$(4x-9)^2*(2x^2+2x+1)^2$

Step-by-step explanation:

(((4x-9)•(((2•(x2))+2x)+1))•(4x-9))•((2x2+2x)+1)

]  (((4x-9)•((2x2+2x)+1))•(4x-9))•(2x2+2x+1)

Trying to factor by splitting the middle term

Factoring  2x2+2x+1

The first term is,  2x2  its coefficient is  2 .

The middle term is,  +2x  its coefficient is  2 .

The last term, "the constant", is  +1

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

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

     -2    +    -1    =    -3

     -1    +    -2    =    -3

     1    +    2    =    3

     2    +    1    =    3

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

 ((4x-9)•(2x2+2x+1)•(4x-9))•(2x2+2x+1)

Multiplying Exponential Expressions:

4.1    Multiply  (4x-9)  by  (4x-9)

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

In our case, the common base is  (4x-9)  and the exponents are :

         1 , as  (4x-9)  is the same number as  (4x-9)1

and   1 , as  (4x-9)  is the same number as  (4x-9)1

The product is therefore,  (4x-9)(1+1) = (4x-9)2

Trying to factor by splitting the middle term

5.1     Factoring  2x2+2x+1

The first term is,  2x2  its coefficient is  2 .

The middle term is,  +2x  its coefficient is  2 .

The last term, "the constant", is  +1

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

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

     -2    +    -1    =    -3

     -1    +    -2    =    -3

     1    +    2    =    3

     2    +    1    =    3

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Multiplying Exponential Expressions:

5.2    Multiply  (2x2+2x+1)  by  (2x2+2x+1)

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

In our case, the common base is  (2x2+2x+1)  and the exponents are :

      1 , as  (2x2+2x+1)  is the same number as  (2x2+2x+1)1

and   1 , as  (2x2+2x+1)  is the same number as  (2x2+2x+1)1

The product is therefore,  (2x2+2x+1)(1+1) = (2x2+2x+1)2

Final result :

 (4x - 9)2 • (2x2 + 2x + 1)2