factorise 16x2– 24x+9
Answers
Answer:
(4x-3)²
Step-by-step explanation:
16x²-24x +9
=(4x)²- 2.4x.3 + (3)²
=(4x-3)²
Answer:(4x-3)x^2
Step-by-step explanation:
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
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