Polynomials: standard form, subtracting, multiplying
Write a polynomial in standard form, subtract with brackets, multiply three terms by two on a grid and raise a product to a power.
- Palestine: grade 7
- Ukraine: grade 7
Guide
Ukrainian Algebra 7 (§§ 6–11) teaches this: the power of a product, monomials, polynomials, and adding, subtracting and multiplying them.
A monomial is in standard form when it has the number (its coefficient) first and then each letter once with its power. In −3x2 the coefficient is −3 and the degree is 2. A polynomial is a sum of monomials; in standard form it has no like terms, and its degree is the highest degree of its terms.
A plus before a bracket: just drop the bracket. A minus: change the sign of every term inside: a − (b − c) = a − b + c.
To multiply polynomials, multiply each term of the first by each term of the second and collect like terms. A grid helps you miss no cell.
Power of a product: (ab)n = anbn; of a quotient: (ab)n = anbn. The index applies to every factor, not only the last one.
Type with the keypad under the mat: digits, letters, ², ³, plus, minus and brackets.