Question

factorise:: 1 - 18a - 63a^2​

Answer 1

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Answer 2

Answer:

STEP1:Equation at the end of step 1

(1 - 18a) - (32•7a2)

STEP2:

STEP3:Pulling out like terms

 3.1     Pull out like factors :

   -63a2 - 18a + 1  =   -1 • (63a2 + 18a - 1) 

Trying to factor by splitting the middle term

 3.2     Factoring  63a2 + 18a - 1 

The first term is,  63a2  its coefficient is  63 .

The middle term is,  +18a  its coefficient is  18 .

The last term, "the constant", is  -1 

Step-1 : Multiply the coefficient of the first term by the constant   63 • -1 = -63 

Step-2 : Find two factors of  -63  whose sum equals the coefficient of the middle term, which is   18 .

     -63   +   1   =   -62     -21   +   3   =   -18     -9   +   7   =   -2     -7   +   9   =   2     -3   +   21   =   18   That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -3  and  21 

                     63a2 - 3a + 21a - 1

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

                    3a • (21a-1)

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

                     1 • (21a-1)

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

                    (3a+1)  •  (21a-1)