Solution - Simplification or other simple results
Other Ways to Solve:
Step by Step Solution
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "x2" was replaced by "x^2".
Step 1 :
Equation at the end of step 1 :
(24x2 - 24x) + 9
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 16x2-24x+9
The first term is, 16x2 its coefficient is 16 .
The middle term is, -24x its coefficient is -24 .
The last term, "the constant", is +9
Step-1 : Multiply the coefficient of the first term by the constant 16 • 9 = 144
Step-2 : Find two factors of 144 whose sum equals the coefficient of the middle term, which is -24 .
| -144 | + | -1 | = | -145 | ||
| -72 | + | -2 | = | -74 | ||
| -48 | + | -3 | = | -51 | ||
| -36 | + | -4 | = | -40 | ||
| -24 | + | -6 | = | -30 | ||
| -18 | + | -8 | = | -26 | ||
| -16 | + | -9 | = | -25 | ||
| -12 | + | -12 | = | -24 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -12 and -12
16x2 - 12x - 12x - 9
Step-4 : Add up the first 2 terms, pulling out like factors :
4x • (4x-3)
Add up the last 2 terms, pulling out common factors :
3 • (4x-3)
Step-5 : Add up the four terms of step 4 :
(4x-3) • (4x-3)
Which is the desired factorization
Multiplying Exponential Expressions :
2.2 Multiply (4x-3) by (4x-3)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (4x-3) and the exponents are :
1 , as (4x-3) is the same number as (4x-3)1
and 1 , as (4x-3) is the same number as (4x-3)1
The product is therefore, (4x-3)(1+1) = (4x-3)2
Final result :
(4x - 3)2
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