factorise (49x^2-126x+81)-31
Answers
Answer:
Equation at the end of step 1 :
(72x2 - 126x) + 81
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 49x2-126x+81
The first term is, 49x2 its coefficient is 49 .
The middle term is, -126x its coefficient is -126 .
The last term, "the constant", is +81
Step-1 : Multiply the coefficient of the first term by the constant 49 • 81 = 3969
Step-2 : Find two factors of 3969 whose sum equals the coefficient of the middle term, which is -126 .
-3969 + -1 = -3970
-1323 + -3 = -1326
-567 + -7 = -574
-441 + -9 = -450
-189 + -21 = -210
-147 + -27 = -174
-81 + -49 = -130
-63 + -63 = -126 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -63 and -63
49x2 - 63x - 63x - 81
Step-4 : Add up the first 2 terms, pulling out like factors :
7x • (7x-9)
Add up the last 2 terms, pulling out common factors :
9 • (7x-9)
Step-5 : Add up the four terms of step 4 :
(7x-9) • (7x-9)
Which is the desired factorization
Multiplying Exponential Expressions :
2.2 Multiply (7x-9) by (7x-9)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (7x-9) and the exponents are :
1 , as (7x-9) is the same number as (7x-9)1
and 1 , as (7x-9) is the same number as (7x-9)1
The product is therefore, (7x-9)(1+1) = (7x-9)2
Final result :
(7x - 9)2
Step-by-step explanation: