Final answer:
Simplifying the expression requires expanding the brackets, combining like terms, and applying algebraic rules including distribution. The resulting simplified form is – 35x2 + 8x – 8 after properly eliminating unnecessary terms and ensuring the solution is valid.
Step-by-step explanation:
To simplify the expression 3x(x – 12x) + 3x2 – 2(x – 2)2, we need to apply standard algebraic techniques such as distribution, combining like terms, and simplifying polynomial expressions.
Firstly, distribute the 3x across the parentheses: 3x×(x – 12x) becomes 3x2 – 36x2.
Then, expand the square: – 2(x – 2)2 becomes – 2(x2 – 4x + 4).
Next, we can simplify the expression by combining like terms and further distributing where necessary:
- 3x2 – 36x2 + 3x2 – 2x2 + 8x – 8
Combine like terms:
Eliminate terms wherever possible and check to see if the simplified expression is reasonable. We are using multiplication, distribution, and combination of like terms to simplify the algebraic expression.