Subtracting polynomials
Subtracting Polynomials teaches Grade 6 students to subtract one polynomial from another by changing the sign of each term in the polynomial being subtracted (distributing the negative sign) and then combining like terms. Covered in Yoshiwara Elementary Algebra Chapter 7: Polynomials, a common source of errors is forgetting to change the signs of all terms when removing the parentheses with a leading minus sign. This skill is the direct extension of combining like terms and polynomial addition.
Key Concepts
Property If an expression in parentheses is preceded by a minus sign, we must change the sign of each term within parentheses when we remove the parentheses. This rule applies when we subtract polynomials.
Examples Subtract $(5x^2 + 4x 1) (2x^2 3x + 4)$. This becomes $5x^2 + 4x 1 2x^2 + 3x 4$, which simplifies to $3x^2 + 7x 5$.
A common mistake is not distributing the negative to all terms, such as writing $5x^2 + 4x 1 2x^2 3x + 4$. This is incorrect.
Common Questions
How do you subtract polynomials?
Change the sign of every term in the polynomial being subtracted, then combine like terms. For example, (3x² + 2x) - (x² - 5x) = 3x² + 2x - x² + 5x = 2x² + 7x.
Why do you change all the signs when subtracting polynomials?
The minus sign before the parentheses is distributed to every term inside, changing each sign. This is an application of the distributive property with -1.
What is the most common mistake when subtracting polynomials?
Only changing the sign of the first term instead of all terms inside the parentheses. Always distribute the negative to every term.
Where is subtracting polynomials in Yoshiwara Elementary Algebra?
This is covered in Chapter 7: Polynomials of Yoshiwara Elementary Algebra.
What is the difference between adding and subtracting polynomials?
When adding, just remove parentheses and combine like terms. When subtracting, first change all signs of the subtracted polynomial, then combine like terms.