(x-2).jpeg "(3x^2+4x-7)(x-2)")
Expanding the Expression: (3x^2 + 4x - 7)(x - 2)
This expression represents the product of two polynomials: a quadratic trinomial (3x^2 + 4x - 7) and a linear binomial (x - 2). To expand this, we can use the distributive property or FOIL method.
Using the Distributive Property
- Step 1: Distribute the first term of the binomial (x) to each term in the trinomial.
- x * (3x^2 + 4x - 7) = 3x^3 + 4x^2 - 7x
- Step 2: Distribute the second term of the binomial (-2) to each term in the trinomial.
- -2 * (3x^2 + 4x - 7) = -6x^2 - 8x + 14
- Step 3: Combine the results from steps 1 and 2.
- 3x^3 + 4x^2 - 7x - 6x^2 - 8x + 14
- Step 4: Simplify by combining like terms.
- 3x^3 - 2x^2 - 15x + 14
Using the FOIL Method
- F: Multiply the first terms of each binomial: (3x^2)(x) = 3x^3
- O: Multiply the outer terms of each binomial: (3x^2)(-2) = -6x^2
- I: Multiply the inner terms of each binomial: (4x)(x) = 4x^2
- L: Multiply the last terms of each binomial: (4x)(-2) = -8x
- Combine: 3x^3 - 6x^2 + 4x^2 - 8x - 7x + 14
- Simplify: 3x^3 - 2x^2 - 15x + 14
The Expanded Form
Therefore, the expanded form of (3x^2 + 4x - 7)(x - 2) is 3x^3 - 2x^2 - 15x + 14.