Question

Find the following using appropriate algebraic identity:

i) (a+5b)2

ii) (2m – 3n)2

iii) (7x+y)(7x–y) iv) (x+6y)(x–4y)

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Answer 1

(a + 5b)²

a² + (5b)² + 2*a*5b

a² + 25b² + 10ab

Identity used : (x+y)² = x² + y² + 2xy

(2m - 3n)²

2m² + (3n)² - 2*2m*3n

4m² + 9n² - 12mn

Identity used : (x-y)² = x² + y² - 2xy

(7x + y)(7x - y)

(7x)² - y²

49x² - y²

Identity used : (a+b)(a-b) = a² - b²

(x+6y)(x–4y)

x(x - 4y) + 6y(x - 4y)

x² - 4xy + 6xy - 24y²

x² + 4xy - 24y²