Question

Your mathematical writing to include full solutions with ju mathematical statements into grammatically correct expo Algebraically manipulate the following expression: (2(x²-2x+5)(2x-2)e²ˣ-(x²-2x+5)²)e^⁽²ˣ⁾²/(e⁴ˣ) ed explanation for each mathematical step written in gram within a 2-column format. Your final answer should follo

Answer 1

To algebraically manipulate the expression (2(x²-2x+5)(2x-2)e²ˣ-(x²-2x+5)²)e^⁽²ˣ⁾²/(e⁴ˣ), expand the terms within the parentheses, distribute the coefficient, simplify the expression, and simplify further by canceling out common factors and simplifying the exponents.

Step-by-step explanation:

To algebraically manipulate the expression:

(2(x²-2x+5)(2x-2)e²ˣ-(x²-2x+5)²)e⁽²ˣ⁾²/(e⁴ˣ)

We can start by expanding the terms within the parentheses:

(2(x²-2x+5)(2x-2)e²ˣ-(x²-2x+5)²)e⁽²ˣ⁾²/(e⁴ˣ) = (2(x²-2x+5)(2x-2)e²ˣ-(x²-4x+4))e⁽²ˣ⁾²/(e⁴ˣ)

Next, distribute the 2 into the terms within the first set of parentheses:

(2x²-4x+10)(2x-2)e²ˣ-(x²-4x+4)e⁽²ˣ⁾²/(e⁴ˣ)

Simplify the expression within the second set of parentheses:

(2x²-4x+10)(2x-2)e²ˣ-(x²-4x+4)e⁽²ˣ⁾²/(e⁴ˣ) = (2x²-4x+10)(2x-2)e²ˣ-(x²-4x+4)e⁽²ˣ⁾²/(e⁴ˣ)

Finally, simplify further by canceling out common factors and simplify the exponents:

(4x³-8x²+20x-4x²+8x-20)e²ˣ-(x²-4x+4)/(e⁴ˣ)