Find the following squares by using the identities.
(i) $(b - 7)^{2}$
(ii) $(x y + 3 z)^{2}$
(iii) $(6 x^{2} - 5 y)^{2}$
(iv) ${(\frac{2}{3} m + \frac{3}{2} n)}^{2}$
(v) $(0.4 p - 0.5 q)^{2}$
(vi) $(2 x y + 5 y)^{2}$

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Solution

i) $(b - 7)^{2}$
$= b^{2} + 7^{2} - 2 (b) (7)$
$= b^{2} + 49 - 14 b$ $∵ [(a - b)^{2}$ $= a^{2} + b^{2} - 2 a b]$

ii) $(x y + 3 z)^{2}$
$= (x y)^{2} + (3 z)^{2} + 2 (x y) (3 z)$
$= x^{2} y^{2} + 9 z^{2} + 6 x y z$ $∵ [(a + b)^{2}$ $= a^{2} + b^{2} + 2 a b]$

iii) $(6 x - 5 y)^{2}$
$= (6 x)^{2} + (5 y)^{2} - 2 (6 x) (5 y)$
$= 36 x^{2} + 25 y^{2} - 60 x y$ $∵ [(a - b)^{2}$ $= a^{2} + b^{2} - 2 a b]$

iv) ${(\frac{2}{3} m + \frac{3}{2} n)}^{2}$
$= {(\frac{2}{3} m)}^{2} + {(\frac{3}{2} n)}^{2} + 2 (\frac{2}{3} m) (\frac{3}{2} n)$
$= \frac{4}{16} m^{2} + \frac{9}{4} n^{2} + 2 m n$ $∵ [(a + b)^{2}$ $= a^{2} + b^{2} + 2 a b]$

v) $(0.4 p - 0.5 q)^{2}$
$= (0.4 p)^{2} + (0.5 q)^{2} - 2 (0.4 p) (0.5 q)$
$= 0.16 p^{2} + 0.25 q^{2} - 4 p q$ $∵ [(a - b)^{2}$ $= a^{2} + b^{2} - 2 a b]$

vi) $(2 x y + 5 y)^{2}$
$= (2 x y)^{2} + (5 y)^{2} + 2 (2 x y) (5 y)$
$= 4 x^{2} y^{2} + 25 y^{2} + 20 x y^{2}$ $∵ [(a + b)^{2}$ $= a^{2} + b^{2} + 2 a b]$
$= y^{2} (4 x^{2} + 20 x + 25)$

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Similar questions

Find the following squares by suing the identities.

(i) (b − 7)²(ii) (xy + 3z)²(iii) (6x² − 5y)²

(iv) (v) (0.4p − 0.5q)²(vi) (2xy + 5y)²

(2 x y + 5 y)^{2}

Question 3(iii)
Find the following squares by using identities:
$(6 x^{2} - 5 y)^{2}$

(2 x y + 5 y)^{2}

(0.4 p + 0.5 q)^{2}

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