The cause of the mistake done was that Andrew did not multiplied the polynomial x² + 4 · x + 8 by the binomial x - 3 correctly, that is, according to algebraic procedures. The correct expanded form is x³ + 4 · x² - 7 · x - 24.
What mistake did Andrew make while expanding a polynomial?
In this problem we must find in which step Andrew did a mistake while expanding the polynomial:
- (x - 3) · (x + 2 + i 2) · (x + 2 - i 2) Given
- (x - 3) · [(x + 2) + i 2] · [(x + 2) - i 2] Associative property
- (x - 3) · [(x + 2)² + 4] a² - b² = (a + b) · (a - b) / Definition of complex number
- (x - 3) · (x² + 4 · x + 8) (a + b)² = a² + 2 · a · b + b² / Associative and commutative property / Definition of addition
- (x - 3) · x² + (x - 3) · (4 · x) + (x - 3) · 8 Distributive property
- x³ - 3 · x + 4 · x² - 12 · x + 8 · x - 24 Distributive property / Multiplication of power of same base / Associative and commutative properties
- x³ + 4 · x² - 7 · x - 24 Distributive property / Definitions of addition and subtraction / Result
The cause of the mistake done was that Andrew did not multiplied the polynomial x² + 4 · x + 8 by the binomial x - 3 correctly, that is, according to algebraic procedures. The correct expanded form is x³ + 4 · x² - 7 · x - 24.
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