Polynomial identities and the Binomial Theorem
Grade 11 Math Worksheet - Building Confidence
Circle the best answer, or write your answer on the line.
Pia squares x² + 3 on a worksheet with an area model of four pieces. Type powers like x^4. What is (x² + 3)²?
In a notebook, Ren draws a square with sides x² − 5 and cuts it into four pieces. Type powers like x^4. What is its area?
Tala expands (x² + 4)² in pencil, piece by piece. Type powers like x^4. What is it in fewest terms?
On a puzzle card, Zee finds the area of a square with sides x² − 6 from its four pieces. What is the area?
On a worksheet, the Pascal row for power 5 is 1, 5, 10, 10, 5, 1. Esme builds the row for power 6. What is its third number?
Kira copies the Pascal row 1, 7, 21, 35, 35, 21, 7, 1 in pencil and starts the row under it. What is the fourth number of the new row?
On a puzzle card, the Pascal row for power 8 is 1, 8, 28, 56, 70, 56, 28, 8, 1. Luz wants the next row. What is its third number?
In a notebook, Noah tests which equation is an identity (true for every value). Which one is it?
- (x³ − 5)² = x⁶ − 5x³ + 25
- (x³ − 5)² = x⁶ + 10x³ + 25
- (x³ − 5)² = x⁶ − 10x³ + 25
- (x³ − 5)² = x⁶ + 25
Pia writes four equations in pencil. Which one is true for every value of the letters?
- (2x² + 3)² = 4x⁴ + 9
- (2x² + 3)² = 4x⁴ + 12x² + 9
- (2x² + 3)² = 4x⁴ − 9
- (2x² + 3)² = 4x⁴ + 6x² + 9
On a puzzle card, Ren must pick the identity (true for every value). Which one is it?
- (x² − 4y)² = x⁴ − 4x²y + 16y²
- (x² − 4y)² = x⁴ + 8x²y + 16y²
- (x² − 4y)² = x⁴ + 16y²
- (x² − 4y)² = x⁴ − 8x²y + 16y²