Step 1 :

Equation in ~ the finish of step 1 : ((0 - 24x2) - 40x) - 25

Step 2 :

Step 3 :

Pulling out prefer terms :3.1 traction out choose factors:-16x2 - 40x - 25=-1•(16x2 + 40x + 25)

Trying to factor by separating the middle term

3.2Factoring 16x2 + 40x + 25 The first term is, 16x2 that is coefficient is 16.The center term is, +40x its coefficient is 40.The last term, "the constant", is +25Step-1 : main point the coefficient the the an initial term by the constant 16•25=400Step-2 : discover two factors of 400 whose sum equates to the coefficient the the middle term, i m sorry 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=40That"s it

Step-3 : Rewrite the polynomial splitting the middle term making use of the two determinants found in step2above, 20 and also 2016x2 + 20x+20x + 25Step-4 : include up the very first 2 terms, pulling out choose factors:4x•(4x+5) include up the critical 2 terms, pulling out typical factors:5•(4x+5) Step-5:Add increase the four terms the step4:(4x+5)•(4x+5)Which is the wanted factorization

Multiplying Exponential Expressions:3.3 multiply (4x+5) by (4x+5)The rule says : To multiply exponential expression which have the same base, include up your exponents.In our case, the typical base is (4x+5) and the index number are:1,as(4x+5) is the exact same number together (4x+5)1and1,as(4x+5) is the same number as (4x+5)1The product is therefore, (4x+5)(1+1) = (4x+5)2