11/20/2020 Lesson Worksheet: Expanding an Expression to a Difference of Two Squares | Nagwa Lesson Worksheet: Expanding an Expression to a Difference of Two Squares Mathematics In this worksheet, we will practice multiplying the sum of two terms by their difference to get the polynomial known as the difference of two squares. Q1: Expand the product (𝑥 + 1)(𝑥 − 1) . A 𝑥 + 1 B 𝑥 − 2𝑥 − 1 C 𝑥 + 2𝑥 − 1 D 𝑥 − 1 E 𝑥 + 2𝑥 + 1 Q2: Use the difference of two squares identity to expand (3𝑎 + 7)(3𝑎 − 7) . A 6𝑎 − 14 B 9𝑎 − 7 C 9𝑎 − 49 D 9𝑎 − 49 E 3𝑎 − 49 Nagwa uses cookies to ensure you get the best experience on our website. Learn about our Privacy Policy. more https://www.nagwa.com/en/worksheets/852189162359/ ACCEPT 1/6 11/20/2020 Lesson Worksheet: Expanding an Expression to a Difference of Two Squares | Nagwa Q3: If 𝑥 − 𝑎 = (𝑥 + 5)(𝑥 − 5) , what is the value of 𝑎 ? Q4: Expand the product (2𝑚 + 𝑛)(2𝑚 − 𝑛) . A 4𝑚 + 2𝑚𝑛 + 𝑛 B 4𝑚 + 2𝑚𝑛 − 𝑛 C 4𝑚 − 2𝑚𝑛 + 𝑛 D 4𝑚 − 𝑛 E 4𝑚 + 𝑛 Q5: If 𝑥 − 𝑦 = 9 and 𝑥 + 𝑦 = 10 , what is the value of 𝑥 − 𝑦 ? Q6: Complete the following: 𝑥 − = (𝑥 − 5) (𝑥 + 5) . Q7: If 𝑥 + 𝑦 = 2 and 𝑥 − 𝑦 = 6 , what is the value of 𝑥 − 𝑦 ? Q8: If 𝑥 + 𝑙 − 25 = (𝑥 + 5)(𝑥 − 5) , what is the value of 𝑙 ? Q9: Given that 𝑛 + 𝑚 = 5 and 𝑛 − 𝑚 = 45 , find 𝑛 − 𝑚 . Q10: If 𝑚 − 𝑛 = 64 and 𝑚 + 𝑛 = 4 , what is the value of 𝑚 − 𝑛 ? Q11: What is the value of √7 + √3 √7 − √3 ? Nagwa uses cookies to ensure you get the best experience on our website. Learn about our Privacy Policy. more https://www.nagwa.com/en/worksheets/852189162359/ ACCEPT 2/6 11/20/2020 Lesson Worksheet: Expanding an Expression to a Difference of Two Squares | Nagwa Q12: Simplify (4𝑧 + 7) (4𝑧 − 7) . A 16𝑧 − 56 − 49 B 16𝑧 + 49 C 16𝑧 + 56 + 49 D 16𝑧 + 56 − 49 E 16𝑧 − 49 Q13: Given that 𝑥 = 2 and 𝑦 = √3 , find the value of 3(𝑥 + 𝑦) (𝑥 − 𝑦) . Q14: Given that 𝑥 − 𝑦 = 62 and 𝑥 − 𝑦 = √31 , find 𝑥 + 𝑦 . A 62√31 B √2 C 2√31 D √31 62 Q15: Expand (2𝑥 − 3)(2𝑥 + 3) . A −4𝑥 − 9 B 4𝑥 − 9 C 4𝑥 + 9 D 4𝑥 + 12𝑥 − 9 E 4𝑥 + 6𝑥 − 9 Q16: Simplify √3 + 2 √3 − 2 . Nagwa uses cookies to ensure you get the best experience on our website. Learn about our Privacy Policy. more https://www.nagwa.com/en/worksheets/852189162359/ ACCEPT 3/6 11/20/2020 Lesson Worksheet: Expanding an Expression to a Difference of Two Squares | Nagwa Q17: What is the area of a rectangle of length (𝑥 + 14) cm and width (𝑥 − 14) cm? A 𝑥 + 196 cm2 B 𝑥 − 196 cm2 C 2𝑥 cm2 D (𝑥 − 14) cm2 E (𝑥 + 14) cm2 Q18: If 𝑥 − 𝑎 = (𝑥 + 10)(𝑥 − 10) , what is the value of 𝑎 ? Q19: If 𝑎 − 𝑏 = 10 and 𝑎 + 𝑏 = 18 , what is the value of 𝑎 − 𝑏 ? Q20: If 𝑚 − 𝑛 = 5 and 𝑚 + 𝑛 = 14 , what is the value of 𝑚 − 𝑛 ? Q21: If 𝑥 + 𝑦 = 9 and 𝑥 − 𝑦 = 6 , what is the value of 𝑥 − 𝑦 ? Q22: Given that 𝑥 + 𝑧 = 3 and 𝑥 − 𝑧 = 3 , find 𝑥 − 𝑧 . Q23: If 𝑥 + 𝑙 − 144 = (𝑥 + 12)(𝑥 − 12) , what is the value of 𝑙 ? Q24: Using the difference of two squares, evaluate 21 × 19 without a calculator. Nagwa uses cookies to ensure you get the best experience on our website. Learn about our Privacy Policy. more https://www.nagwa.com/en/worksheets/852189162359/ ACCEPT 4/6 11/20/2020 Lesson Worksheet: Expanding an Expression to a Difference of Two Squares | Nagwa Q25: Use the identity (𝑥 − 𝑦)(𝑥 + 𝑦) = 𝑥 − 𝑦 to evaluate 33 − 31 without using a calculator. Lesson Lesson Video Lesson Explainer Lesson Worksheet Related Lessons Expanding an Expression to a Difference of Two Squares Squaring Binomials Multiplying Binomials Factoring Monic Quadratics Simplifying Expressions: Combining Like Terms Difference of Two Squares Factoring Nonmonic Quadratics Factoring by Grouping Factorization Using the Highest Common Factor Factoring Perfect-Square Trinomials About Us • Contact Us • Privacy Policy • Terms and Conditions • Careers • Courses • Lessons • Plans • Videos Explainers Worksheets User Guide Learn • Portals • Nagwa uses cookies to ensure you• get the best •experience on•our website. about our Privacy Policy. Memberships • Apps more https://www.nagwa.com/en/worksheets/852189162359/ ACCEPT 5/6 11/20/2020 Lesson Worksheet: Expanding an Expression to a Difference of Two Squares | Nagwa Copyright © 2020 Nagwa All Rights Reserved Nagwa uses cookies to ensure you get the best experience on our website. Learn about our Privacy Policy. more https://www.nagwa.com/en/worksheets/852189162359/ ACCEPT 6/6
