Learnify Academy is a tuition centre in Bahrain. Classes are for students in Bahrain only.Tuition classes in Bahrain only

Algebraic identities · 2 marks

Let us try to expand (5x + 2y)2.

Answer: (5x + 2y)2 = 25x2 + 20xy + 4y2

Step-by-step solution

Given: (5x + 2y)2
To find: Its expansion

Idea: Use (a + b)2 = a2 + 2ab + b2 with a = 5x and b = 2y. a and b can be whole terms, not just single letters.

  1. Compare (5x + 2y)2 with (a + b)2: a = 5x, b = 2y.½ mark
  2. (5x + 2y)2 = (5x)2 + 2(5x)(2y) + (2y)2½ mark
  3. (5x)2 = 25x2; 2 × 5x × 2y = 20xy; (2y)2 = 4y2½ mark
  4. = 25x2 + 20xy + 4y2½ mark
(5x + 2y)² = 25x² + 20xy + 4y².

Check: Put x = 1, y = 1: (5 + 2)2 = 49 and 25 + 20 + 4 = 49 ✓.

Answer to write in the exam

(5x + 2y)2 = (5x)2 + 2(5x)(2y) + (2y)2 [(a + b)2 = a2 + 2ab + b2]

∴ (5x + 2y)2 = 25x2 + 20xy + 4y2

Common mistakes that cost marks

  • Writing (5x)2 = 5x2. Both the 5 and the x are squared: 25x2.
  • Writing the answer as 25x2 + 4y2, missing the middle term 20xy.
  • Writing the middle term as 10xy (forgetting the 2 in 2ab).

How this can come in the exam

MCQ (1 mark)

(4m + 3n)2 equals

  1. 16m2 + 9n2
  2. 16m2 + 12mn + 9n2
  3. 16m2 + 24mn + 9n2
  4. 4m2 + 24mn + 3n2
Show answer

(C) 16m2 + 24mn + 9n2
(4m)2 + 2(4m)(3n) + (3n)2 = 16m2 + 24mn + 9n2.

Assertion–Reason (1 mark)

Assertion (A): (5x + 2y)2 = 25x2 + 4y2.
Reason (R): (a + b)2 = a2 + 2ab + b2.

  1. Both A and R are true, and R is the correct explanation of A.
  2. Both A and R are true, but R is not the correct explanation of A.
  3. A is true but R is false.
  4. A is false but R is true.
Show answer

(D) A is false but R is true.
R is the correct identity, and it shows A is missing the middle term 20xy, so A is false.

Try one yourself

Expand (3p + 7q)2.

Show answer

(3p)2 + 2(3p)(7q) + (7q)2 = 9p2 + 42pq + 49q2.

More questions like this

All Algebraic identities questions · All maths questions

← 1. What can you say about a and b if (a + b)² < a² + b²? 2. What can yTo calculate 43², we can write it as (40 + 3)². →