Factorize:
L. 144a+ + 24 + 1
Answers
Answer:
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Step-by-step explanation:
Factoring 144a2+24a+1
The first term is, 144a2 its coefficient is 144 .
The middle term is, +24a its coefficient is 24 .
The last term, "the constant", is +1
Step-1 : Multiply the coefficient of the first term by the constant 144 • 1 = 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 -9 + -16 = -25 -8 + -18 = -26 -6 + -24 = -30 -4 + -36 = -40 -3 + -48 = -51 -2 + -72 = -74 -1 + -144 = -145 1 + 144 = 145 2 + 72 = 74 3 + 48 = 51 4 + 36 = 40 6 + 24 = 30 8 + 18 = 26 9 + 16 = 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
144a2 + 12a + 12a + 1
Step-4 : Add up the first 2 terms, pulling out like factors :
12a • (12a+1)
Add up the last 2 terms, pulling out common factors :
1 • (12a+1)
Step-5 : Add up the four terms of step 4 :
(12a+1) • (12a+1)
Which is the desired factorizatio
2.2 Multiply (12a+1) by (12a+1)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (12a+1) and the exponents are :
1 , as (12a+1) is the same number as (12a+1)1
and 1 , as (12a+1) is the same number as (12a+1)1
The product is therefore, (12a+1)(1+1) = (12a+1)2
Final result :