Equation at the end of step 1 : (24x2 + 40x) + 25
Step 2 :Trying to factor by splitting the middle term
2.1 Factoring 16x2+40x+25
The first term is, 16x2 its coefficient is 16 .
The middle term is, +40x its coefficient is 40 .
The last term, "the constant", is +25
Step-1 : Multiply the coefficient of the first term by the constant 16 • 25 = 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
16x2 + 20x + 20x + 25
Step-4 : Add up the first 2 terms, pulling out like factors :
4x • (4x+5)
Add up the last 2 terms, pulling out common factors :
5 • (4x+5)
Step-5 : Add up the four terms of step 4 :
(4x+5) • (4x+5)
Which is the desired factorization
Multiplying Exponential Expressions :
2.2 Multiply (4x+5) by (4x+5)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (4x+5) and the exponents are :
1 , as (4x+5) is the same number as (4x+5)1
and 1 , as (4x+5) is the same number as (4x+5)1
The product is therefore, (4x+5)(1+1) = (4x+5)2
Final result :
(4x + 5)2
hope this helps hope i am brainliest i need it
