Question

Factorise
169n*2 - 52n+4

Answer 1

Explanation:

169n2+52n+4

Final result :

(13n + 2)2

Step by step solution :

Step 1 :

Equation at the end of step 1 :

(132n2 + 52n) + 4

Step 2 :

Trying to factor by splitting the middle term

2.1 Factoring 169n2+52n+4

The first term is, 169n2 its coefficient is 169 .

The middle term is, +52n its coefficient is 52 .

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

Step-1 : Multiply the coefficient of the first term by the constant 169 • 4 = 676

Step-2 : Find two factors of 676 whose sum equals the coefficient of the middle term, which is 52 .

-676 + -1 = -677

-338 + -2 = -340

-169 + -4 = -173

-52 + -13 = -65

-26 + -26 = -52

-13 + -52 = -65

-4 + -169 = -173

-2 + -338 = -340

-1 + -676 = -677

1 + 676 = 677

2 + 338 = 340

4 + 169 = 173

13 + 52 = 65

26 + 26 = 52 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 26 and 26

169n2 + 26n + 26n + 4

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

13n • (13n+2)

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

2 • (13n+2)

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

(13n+2) • (13n+2)

Which is the desired factorization

Multiplying Exponential Expressions :

2.2 Multiply (13n+2) by (13n+2)

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

In our case, the common base is (13n+2) and the exponents are :

1 , as (13n+2) is the same number as (13n+2)1

and 1 , as (13n+2) is the same number as (13n+2)1

The product is therefore, (13n+2)(1+1) = (13n+2)2

Final result :

(13n + 2)2