factorise the algebraic expressions 32x^2+ 48x + 18
Answers
Step-By-Step Explanation =
Step 1: (25x2 + 48x) + 18
Step 2: Pull out like factors :
32x2 + 48x + 18 = 2 • (16x2 + 24x + 9)
Step 3: 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 .
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)
Step 5 : Add up the four terms of step 4 :
(4x+3) • (4x+3)
Which is the desired factorization
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 :
2 • (4x + 3)2