2%2B4x2(x-7)-4(x-2)3.jpeg "(2x-3)2+4x2(x-7) 4(x-2)3")
Simplifying the Expression: (2x-3)2 + 4x2(x-7) 4(x-2)3
This expression involves multiple terms with exponents and parentheses. To simplify it, we need to follow the order of operations (PEMDAS/BODMAS) and apply the necessary algebraic rules.
Step 1: Expand the powers
- (2x-3)2: This is a binomial squared, which expands as (2x-3)(2x-3) using the FOIL method:
- First: (2x)(2x) = 4x²
- Outer: (2x)(-3) = -6x
- Inner: (-3)(2x) = -6x
- Last: (-3)(-3) = 9
- Combining like terms: 4x² - 12x + 9
- 4(x-2)3: This represents 4 multiplied by the cube of (x-2). Expanding the cube:
- (x-2)3 = (x-2)(x-2)(x-2)
- Using the distributive property (or FOIL method) repeatedly, we get: x³ - 6x² + 12x - 8
- Multiplying by 4: 4x³ - 24x² + 48x - 32
Step 2: Simplify the entire expression
Now we have: (4x² - 12x + 9) + 4x²(x-7) + (4x³ - 24x² + 48x - 32)
- Distribute 4x²: 4x² (x-7) = 4x³ - 28x²
- Combine like terms:
- x³ terms: 4x³ + 4x³ = 8x³
- x² terms: 4x² - 28x² - 24x² = -48x²
- x terms: -12x + 48x = 36x
- Constant terms: 9 - 32 = -23
Step 3: Final simplified expression
Therefore, the simplified expression is: 8x³ - 48x² + 36x - 23