Evaluate:
(i) $(4 x + 2 y)^{2}$
(ii) $(5 x - y)^{2}$
(iii) $(3 x + 7 y) (3 x - 7 y)$

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Solution

(i) We have,
$(4 x + 2 y)^{2} = (4 x)^{2} + 2 \times (4 x) \times (2 y) + (2 y)^{2}$
[Using: $(a + b)^{2} = a^{2} + 2 a b + b^{2}$ ]
$= 16 x^{2} + 16 x y + 4 y^{2}$
(ii) We have,
$(5 x - y)^{2} = (5 x)^{2} - 2 \times (5 x) \times (y) + (y)^{2}$
[Using: $(a - b)^{2} = a^{2} - 2 a b + b^{2}$ ]
$= 25^{2} - 10 x y + y^{2}$
(iii) We have,
$(3 x + 7 y) (3 x - 7 y) = (3 x^{2} - (7 y)^{2}$
[Using: $(a + b) (a - b) = a^{2} - b^{2}$ ]
$(3 x + 7 y) (3 x - 7 y) = 9 x^{2} - 49 y^{2}$

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Similar questions

81 x^{2} - 49 y^{2}

Which of the pairs given in options will add up to give $9 x + 5 y$ ?

(4 x - 7 y) (2 y + 3 x)

5 x - 3 y = 2

4 x - 7 y = - 3

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