What should be added to make each of the following perfect square: 9a^2-24a+16
Answers
Answer:
(32a2 - 24a) + 16
Factoring 9a2-24a+16
The first term is, 9a2 its coefficient is 9 .
The middle term is, -24a its coefficient is -24 .
The last term, "the constant", is +16
Step-1 : Multiply the coefficient of the first term by the constant 9 • 16 = 144
Step-2 : Find two factors of 144 whose sum equals the coefficient of the middle term, which is -24 .
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -12 and -12
9a2 - 12a - 12a - 16
Step-4 : Add up the first 2 terms, pulling out like factors :
3a • (3a-4)
Add up the last 2 terms, pulling out common factors :
4 • (3a-4)
Step-5 : Add up the four terms of step 4 :
(3a-4) • (3a-4)
Which is the desired factorization
Multiply (3a-4) by (3a-4)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (3a-4) and the exponents are :
1 , as (3a-4) is the same number as (3a-4)1
and 1 , as (3a-4) is the same number as (3a-4)1
The product is therefore, (3a-4)(1+1) = (3a-4)2
Final result-(3a - 4)2