Given: The algebraic expression 3x(x – 12x) + 3x² – 2(x – 2)² --------(i)
To prove: The final simplified product = –28x² +8x – 8.
Solution:
Step No. 1
First, we shall expand the term (x – 2)² by using Identity (a-b)²= a² + b² - 2ab
So, (x – 2)² = x² + 4 - 4x
From given expression (i)
3x(x – 12x) + 3x² – 2(x² + 4 - 4x) --------(ii)
Step No. 2
Now, we shall multiply by the terms within the parentheses in (ii)
(3x² – 36x²) + 3x² – (2x² + 8 - 8x) --------(iii)
Step No. 3
Now, we shall simplify the terms within the parentheses in (iii)
(– 33x²) + 3x² – (2x² + 8 - 8x) --------(iv)
Step No. 4
Now, we shall open the parentheses to eliminate parentheses in (iv)
– 33x² + 3x² – 2x² - 8 + 8x --------(v)
Step No. 5
Now, we shall add and subtract the like terms in (v)
– 28x² + 8x -8 --------(vi)
Hence, the simplified expression will be – 28x² + 8x -8
