Question

factorise 49x²+70x+25​

Answer 1

Answer:

49x²+70x+25

(7x)² + 2(7x)(5) + (5)²

(7x + 5)²

Answer is (7x + 5)²

Answer 2

Answer: (7x-5)²

Step-by-step explanation:

-Equation at the end of step 1

(72x2 -  70x) +  25

STEP  2-

Trying to factor by splitting the middle term

Factoring  49x2-70x+25  

The first term is,  49x2  its coefficient is  49 .

The middle term is,  -70x  its coefficient is  -70 .

The last term, "the constant", is  +25  

Step-1 : Multiply the coefficient of the first term by the constant   49 • 25 = 1225  

Step-2 : Find two factors of  1225  whose sum equals the coefficient of the middle term, which is   -70 .

     -1225    +    -1    =    -1226  

     -245    +    -5    =    -250  

     -175    +    -7    =    -182  

     -49    +    -25    =    -74  

     -35    +    -35    =    -70    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -35  and  -35  

                    49x2 - 35x - 35x - 25

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

                   7x • (7x-5)

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

                   5 • (7x-5)

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

                   (7x-5)  •  (7x-5)

            Which is the desired factorization