show that (2x+5)^ - (2x-5)^ = 40x
Answers
Answer:
Equation at the end of step 1
((2•(x5))-(2•(x4)))-(23•5x3)
STEP
2
:
Equation at the end of step
2
:
((2 • (x5)) - 2x4) - (23•5x3)
STEP
3
:
Equation at the end of step
3
:
(2x5 - 2x4) - (23•5x3)
STEP
4
:
STEP
5
:
Pulling out like terms
5.1 Pull out like factors :
2x5 - 2x4 - 40x3 = 2x3 • (x2 - x - 20)
Trying to factor by splitting the middle term
5.2 Factoring x2 - x - 20
The first term is, x2 its coefficient is 1 .
The middle term is, -x its coefficient is -1 .
The last term, "the constant", is -20
Step-1 : Multiply the coefficient of the first term by the constant 1 • -20 = -20
Step-2 : Find two factors of -20 whose sum equals the coefficient of the middle term, which is -1 .
-20 + 1 = -19
-10 + 2 = -8
-5 + 4 = -1 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -5 and 4
x2 - 5x + 4x - 20
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-5)
Add up the last 2 terms, pulling out common factors :
4 • (x-5)
Step-5 : Add up the four terms of step 4 :
(x+4) • (x-5)
Which is the desired factorization
Step-by-step explanation:
Answer:
Step-by-step explanation:
2x + 5x5 - 40x = 2x - 5x5
2x + 25 - 40x = 2x - 25
25 - 40x - 2x = 2x - 25
25 - x(40-2)= 2x - 25
25 - 38x = 2x - 25
= 2x + 38x - 25 -25
=x(2 + 38) -0
=40x