Polynomials
Addition:
(2x²y³ - 3xy² - 4x³y) + (6xy² - x³y + 3xy²)
Find common terms and add them together.
Keep in mind; you are only adding the numerical coefficients (no change to the exponents)
= (2x²y³ + 6xy² - 5x³y)
Subtraction:
Subtract (5x² + 3xy² - 7xy) from (3xy – 2xy² - 2)
= (3xy – 2xy² - 2) - (5x² + 3xy² - 7xy)
= (10xy – 5xy² - 5x² -2)
Multiplication:
(2xy² - 3x)² This square² stipulates that we will be multiplying the entire content of the bracket by itself.
(2xy² - 3x) (2xy² - 3x)
2xy² (2xy² - 3x) -3x (2xy² - 3x)
When multiplying polynomials, ADD EXPONENTS together and MULTIPLY NUMERICAL COEFFICIENTS.
(Make sure to verify your positive and negative numbers at ALL times)
4x²y³ – 6x²y²- 6x²y²+ 9x²
Now apply the addition rules here; find common terms and add them together.
4x²y³ – 6x²y² - 6x²y²+ 9x²
= 4x²y³ – 12x²y² + 9x²
Division:
(-28x³ y² + 7x²y³ ) ÷ 4x²y²
Divide each monomial in the brackets by the monomial outside.
When dividing polynomials, SUBTRACT EXPONENTS and DIVIDE NUMERICAL COEFFICIENTS.
-28x³y² + 7x²y³
4x²y² 4x²y²
= -7x + 7y
4
Addition:
(2x²y³ - 3xy² - 4x³y) + (6xy² - x³y + 3xy²)
Find common terms and add them together.
Keep in mind; you are only adding the numerical coefficients (no change to the exponents)
= (2x²y³ + 6xy² - 5x³y)
Subtraction:
Subtract (5x² + 3xy² - 7xy) from (3xy – 2xy² - 2)
= (3xy – 2xy² - 2) - (5x² + 3xy² - 7xy)
= (10xy – 5xy² - 5x² -2)
Multiplication:
(2xy² - 3x)² This square² stipulates that we will be multiplying the entire content of the bracket by itself.
(2xy² - 3x) (2xy² - 3x)
2xy² (2xy² - 3x) -3x (2xy² - 3x)
When multiplying polynomials, ADD EXPONENTS together and MULTIPLY NUMERICAL COEFFICIENTS.
(Make sure to verify your positive and negative numbers at ALL times)
4x²y³ – 6x²y²- 6x²y²+ 9x²
Now apply the addition rules here; find common terms and add them together.
4x²y³ – 6x²y² - 6x²y²+ 9x²
= 4x²y³ – 12x²y² + 9x²
Division:
(-28x³ y² + 7x²y³ ) ÷ 4x²y²
Divide each monomial in the brackets by the monomial outside.
When dividing polynomials, SUBTRACT EXPONENTS and DIVIDE NUMERICAL COEFFICIENTS.
-28x³y² + 7x²y³
4x²y² 4x²y²
= -7x + 7y
4