P.
using identities factorise
25 m2+40m+16
Answers
Answer: (5m + 4)2
Step-by-step explanation: Changes made to your input should not affect the solution:
(1): "m2" was replaced by "m^2".
STEP
1
:
Equation at the end of step 1
(52m2 + 40m) + 16
STEP
2
:
Trying to factor by splitting the middle term
2.1 Factoring 25m2+40m+16
The first term is, 25m2 its coefficient is 25 .
The middle term is, +40m its coefficient is 40 .
The last term, "the constant", is +16
Step-1 : Multiply the coefficient of the first term by the constant 25 • 16 = 400
Step-2 : Find two factors of 400 whose sum equals the coefficient of the middle term, which is 40 .
-400 + -1 = -401
-200 + -2 = -202
-100 + -4 = -104
-80 + -5 = -85
-50 + -8 = -58
-40 + -10 = -50
-25 + -16 = -41
-20 + -20 = -40
-16 + -25 = -41
-10 + -40 = -50
-8 + -50 = -58
-5 + -80 = -85
-4 + -100 = -104
-2 + -200 = -202
-1 + -400 = -401
1 + 400 = 401
2 + 200 = 202
4 + 100 = 104
5 + 80 = 85
8 + 50 = 58
10 + 40 = 50
16 + 25 = 41
20 + 20 = 40 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 20 and 20
25m2 + 20m + 20m + 16
Step-4 : Add up the first 2 terms, pulling out like factors :
5m • (5m+4)
Add up the last 2 terms, pulling out common factors :
4 • (5m+4)
Step-5 : Add up the four terms of step 4 :
(5m+4) • (5m+4)
Which is the desired factorization
Multiplying Exponential Expressions:
2.2 Multiply (5m+4) by (5m+4)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (5m+4) and the exponents are :
1 , as (5m+4) is the same number as (5m+4)1
and 1 , as (5m+4) is the same number as (5m+4)1
The product is therefore, (5m+4)(1+1) = (5m+4)2
Final result :
(5m + 4)2