PRACTICE QUESTION FOR a PLUS b WHOLE SQUARE

(a+b)² = a²+2ab+b²

Problem 1 :

Expand (3x + 7y)² 

(A) x² + 42xy + 49y²    (B) 9x² + 42xy + 49y²

(C) 9x² - 42xy - 9y²

Problem 2 :

Expand (2x + 3y)²

 (A)  4x^²+12xy+9y^²  (B)  16x^²+42xy+49y^²

 (C)  9x^²+12xy-9y^²

Problem 3 :

Expand (2a + 3b)²

 (A) 4a^²+12ab+9b^²  (B) 16a^²+25ab+49b^² 

(C)  9a^²+42ab+9b^²

Problem 4 :

Expand (a + 5b)²

(A) a^² + 10 ab + 25 b^²  (B)  9a^² + 25 ab + 16 b^²

(C)  9a^² +12 ab + 9 b^²

Problem 5 :

Expand (3p + 5q)²

(A) 3p^² + 40 pq + 25 q^²   (B) p^² + 30 pq + 49 q^²

(C)  9p^² +30 pq + 25 q^²

Problem 6 :

Expand (5c + 7d)²

(A) 5c^² + 35cd + 7d^²  (B) 5c^² - 35cd + 7d^²

(C)  25c^² + 70cd + 49d^²

Solutions for the Above Practice Questions

Problem 1 :

Expand (3x + 7y)² 

Solution :

(a + b)² = a² + 2 a b + b²

Here a  =  3x and b  =  7y

(3x + 7y)²  =  (3x)² + 2(3x)(7y) + (7y)²

  =  9x²+42xy+49y²

Problem 2 :

Expand (2x + 3y)² 

Solution :

Here a  =  2x and b  =  3y

(2x + 3y)²  =  (2x)²+2(2x)(3y)+(3y)²

=  4x²+12xy+9y²

Problem 3 :

Expand (2a + 3b)²

Solution :

Here a  =  2a and b  =  3b

(2a + 3b)²  =  (2a)² + 2 (2a)(3b) + (3b)²

=  4a² + 12 a b + 9 b²

Problem 4 :

Expand (a + 5b)²

Solution :

Here a  =  a and b  =  5b

(a + 5b)²  =  (a)² + 2 (a)(5b) + (5b)²

=  a² + 10 a b + 25 b²

Problem 5 :

Expand (3p + 5q)²

Solution :

here a  =  3p and b  =  5q

(3p + 5q)²  =  (3p)² + 2(3p)(5q) + (5q)²

  =  9p² + 30 pq + 25q²

Problem 6 :

Expand (5c + 7d)²

Solution :

here a  =  5c and b  =  7d

(5c + 7d)²  =  (5c)² + 2(5c)(7d) + (7d)²

  =  25c² + 70 cd + 49d²

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