Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(26u2 + 48u) + 9
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 64u2+48u+9
The first term is, 64u2 its coefficient is 64 .
The middle term is, +48u its coefficient is 48 .
The last term, "the constant", is +9
Step-1 : Multiply the coefficient of the first term by the constant 64 • 9 = 576
Step-2 : Find two factors of 576 whose sum equals the coefficient of the middle term, which is 48 .
| -576 | + | -1 | = | -577 | ||
| -288 | + | -2 | = | -290 | ||
| -192 | + | -3 | = | -195 | ||
| -144 | + | -4 | = | -148 | ||
| -96 | + | -6 | = | -102 | ||
| -72 | + | -8 | = | -80 | ||
| -64 | + | -9 | = | -73 | ||
| -48 | + | -12 | = | -60 | ||
| -36 | + | -16 | = | -52 | ||
| -32 | + | -18 | = | -50 | ||
| -24 | + | -24 | = | -48 | ||
| -18 | + | -32 | = | -50 | ||
| -16 | + | -36 | = | -52 | ||
| -12 | + | -48 | = | -60 | ||
| -9 | + | -64 | = | -73 | ||
| -8 | + | -72 | = | -80 | ||
| -6 | + | -96 | = | -102 | ||
| -4 | + | -144 | = | -148 | ||
| -3 | + | -192 | = | -195 | ||
| -2 | + | -288 | = | -290 | ||
| -1 | + | -576 | = | -577 | ||
| 1 | + | 576 | = | 577 | ||
| 2 | + | 288 | = | 290 | ||
| 3 | + | 192 | = | 195 | ||
| 4 | + | 144 | = | 148 | ||
| 6 | + | 96 | = | 102 | ||
| 8 | + | 72 | = | 80 | ||
| 9 | + | 64 | = | 73 | ||
| 12 | + | 48 | = | 60 | ||
| 16 | + | 36 | = | 52 | ||
| 18 | + | 32 | = | 50 | ||
| 24 | + | 24 | = | 48 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 24 and 24
64u2 + 24u + 24u + 9
Step-4 : Add up the first 2 terms, pulling out like factors :
8u • (8u+3)
Add up the last 2 terms, pulling out common factors :
3 • (8u+3)
Step-5 : Add up the four terms of step 4 :
(8u+3) • (8u+3)
Which is the desired factorization
Multiplying Exponential Expressions :
2.2 Multiply (8u+3) by (8u+3)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (8u+3) and the exponents are :
1 , as (8u+3) is the same number as (8u+3)1
and 1 , as (8u+3) is the same number as (8u+3)1
The product is therefore, (8u+3)(1+1) = (8u+3)2
Final result :
(8u + 3)2
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