The FOIL method, standing for First, Outer, Inner, Last, is a technique utilized for the multiplication of binomials. It involves multiplying the First terms in each of the binomials, followed by the Outer, Inner, and Last terms. The final step involves adding all the results together, and simplifying any similar terms. This method is particularly useful when it comes to expanding and simplifying expressions involving polynomials.
| Topic | Problem | Solution |
|---|---|---|
| None | \( (2 x-1)(2 x-1) \) | \( (2x - 1)(2x - 1) \) |
| None | $(x+4)(x+6)(-(x-1)(x+7)$ | Given the expression $(x+4)(x+6)(-(x-1)(x+7)$, we need to simplify it. |
| None | b) Expand and simplify $2 x(3 x-5)+x(x-1)$ | Expand the given expression: \(2x(3x-5)+x(x-1) = 2x(3x) - 2x(5) + x(x) - x(1)\) |
| None | 9. Multiply the polynomials. \[ \left(4 b^{2} z^{… | \( (4 b^{2} z^{2} + 4 b z) (-2 b^{3} z - 2 z^{3} + 6 z^{2} + 5 z) \) |
| None | Expand each of the following products. Your answe… | The question is asking to expand the given expressions. This can be done by applying the distributi… |
| None | Expand the following product. \[ \left(x^{2}-x-1\… | We are given the product of two polynomials: \(\left(x^{2}-x-1\right)\left(x^{2}+7 x+12\right)\). |
| None | Express as a trinomial. \[ (x+4)(2 x+9) \] | \( (x+4)(2x+9) = x(2x+9) + 4(2x+9) \) |
| None | Question 4 ( 2 points) Expand and simplify $(x+5)… | The question is asking to expand and simplify the expression \((x+5)(x+6)\). This is a simple binom… |
| None | Rewrite without parentheses and simplify. \[ (w-6… | (w-6)^2 = (w-6)(w-6) |