In this Grade 6 lesson from Yoshiwara Elementary Algebra, students review the key concepts from Chapter 7, including polynomial operations, the laws of exponents, factoring techniques such as the GCF and box method, and special products like squares of binomials and the difference of two squares. Students practice expanding expressions such as (a + b)² and (a − b)³, factoring quadratic trinomials and sums or differences of cubes, and distinguishing between factorable and non-factorable expressions like x² − 4 versus x² + 4. The lesson consolidates understanding through evaluation tables and area models to test equivalence and verify algebraic identities.
Section 1
📘 Polynomials: A Comprehensive Review
This review consolidates your skills with polynomials. You'll master adding, subtracting, multiplying, and factoring—key tools for simplifying expressions. We'll revisit special products like and their factorizations.
Soon, you'll work through practice cards and challenge problems covering all polynomial operations and factoring methods.
Section 2
Polynomials
• A polynomial is a sum of terms, each of which is a power of a variable with a constant coefficient and a whole number exponent.
• The degree of a polynomial in one variable is the largest exponent that appears in any term.
• Like terms are any terms that are exactly alike in their variable factors. The exponents on the variable factors must also match.
Section 3
First law of exponents
To multiply two powers with the same base, we add the exponents and leave the base unchanged. In symbols,
Section 4
Second law of exponents
To divide two powers with the same base, we subtract the smaller exponent from the larger one, and keep the same base.
Section 5
Special products
Squares of Binomials.
Section 6
Special factorizations
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter
Expand to review the lesson summary and core properties.
Section 1
📘 Polynomials: A Comprehensive Review
This review consolidates your skills with polynomials. You'll master adding, subtracting, multiplying, and factoring—key tools for simplifying expressions. We'll revisit special products like and their factorizations.
Soon, you'll work through practice cards and challenge problems covering all polynomial operations and factoring methods.
Section 2
Polynomials
• A polynomial is a sum of terms, each of which is a power of a variable with a constant coefficient and a whole number exponent.
• The degree of a polynomial in one variable is the largest exponent that appears in any term.
• Like terms are any terms that are exactly alike in their variable factors. The exponents on the variable factors must also match.
Section 3
First law of exponents
To multiply two powers with the same base, we add the exponents and leave the base unchanged. In symbols,
Section 4
Second law of exponents
To divide two powers with the same base, we subtract the smaller exponent from the larger one, and keep the same base.
Section 5
Special products
Squares of Binomials.
Section 6
Special factorizations
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter