Question

factorise 16 X square - 24 x + 9​

Answer 1

Step-by-step explanation:

${16x}^{2} - 24x + 9$

=

${(4x)}^{2} - 2 \times 4 \times 3 + {3}^{2}$

=

${(4x - 3)}^{2}$

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Answer 2

Answer:

Step-by-step explanation:

STEP 1 : Equation at the end of step 1

 (24x2 -  24x) +  9

STEP 2 : Trying to factor by splitting the middle term

2.1     Factoring  16x2-24x+9  

The first term is,  16x2  its coefficient is  16 .

The middle term is,  -24x  its coefficient is  -24 .

The last term, "the constant", is  +9  

Step-1 : Multiply the coefficient of the first term by the constant   16 • 9 = 144  

Step-2 : Find two factors of  144  whose sum equals the coefficient of the middle term, which is   -24 .

     -144    +    -1    =    -145  

     -72    +    -2    =    -74  

     -48    +    -3    =    -51  

     -36    +    -4    =    -40  

     -24    +    -6    =    -30  

     -18    +    -8    =    -26  

     -16    +    -9    =    -25  

     -12    +    -12    =    -24    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -12  and  -12  

                    16x2 - 12x - 12x - 9

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

                   4x • (4x-3)

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

                   3 • (4x-3)

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

                   (4x-3)  •  (4x-3)

            Which is the desired factorization

Multiplying Exponential Expressions:

2.2    Multiply  (4x-3)  by  (4x-3)  

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

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

         1 , as  (4x-3)  is the same number as  (4x-3)^1  

and   1 , as  (4x-3)  is the same number as  (4x-3)^1  

The product is therefore,  (4x-3)(1+1) = (4x-3)^2