Question

Simplify the expression to a polynomial in standard form: (3x² - 4x + 1)(-2x² + 4x + 1)

A) 6x⁴ - 8x³ - x² + 16x - 4
B) -6x⁴ + 8x³ + x² - 16x + 4
C) 6x⁴ - 8x³ - x² - 16x + 4
D) -6x⁴ + 8x³ + x² + 16x - 4

Answer 1

B) -6x⁴ + 8x³ + x² - 16x + 4

To simplify the expression (3x² - 4x + 1)(-2x² + 4x + 1) to a polynomial in standard form, we can use the distributive property.

Step-by-step explanation:

To simplify the expression (3x² - 4x + 1)(-2x² + 4x + 1) to a polynomial in standard form, we can use the distributive property to multiply each term of the first polynomial by each term of the second polynomial.

Step 1: Multiply 3x² by each term of the second polynomial: 3x² * -2x² + 3x² * 4x + 3x² * 1

Step 2: Multiply -4x by each term of the second polynomial: -4x * -2x² + -4x * 4x + -4x * 1

Step 3: Multiply 1 by each term of the second polynomial: 1 * -2x² + 1 * 4x + 1 * 1

Step 4: Combine like terms: -6x⁴ + 8x³ + x² - 16x + 4