Q. 204.4( 7 Votes )

# Show that:

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Answer :

(i)

L.H.S = (3x + 7)^{2} – 84x

= (3x)^{2} + (7)^{2} + 2 (3x) (7) – 84x

= (3x)^{2} + (7)^{2} + 42x – 84x

= (3x)^{2} + (7)^{2} – 42x

= (3x)^{2} + (7)^{2} – 2 (3x) (7)

= (3x – 7)^{2}

= R.H.S

Hence, proved

L.H.S = (9a – 5b)^{2} + 180ab

= (9a)^{2} + (5b)^{2} – 2 (9a) (5b) + 180ab

= (9a)^{2} 6 (5b)^{2} – 90ab + 180ab

= (9a)^{2} + (5b)^{2} + 9ab

= (9a)^{2} + (5b)^{2} + 2 (9a) (5b)

= (9a + 5b)^{2}

= R.H.S

Hence, proved

L.H.S = ( - )^{2} + 2mn

= ()^{2} + ()^{2} – 2mn + 2mn

= ()^{2} + ()^{2}

= m^{2} + n^{2}

= R.H.S

Hence, verified

L.H.S = (4pq + 3q)^{2} – (4pq – 3q)^{2}

= (4pq)^{2} + (3q)^{2} + 2 (4pq) (3q) – (4pq)^{2} – (3q)^{2} + 24pq^{2}

= 24pq^{2} + 24pq^{2}

= 48pq^{2}

Hence, proved

L.H.S = (a – b) (a + b) + (b – c) (b + c) + (c – a) (c + a)

Using identity:

(a – b) (a + b) = a^{2} – b^{2}

We get,

= (a^{2} – b^{2}) + (b^{2} – c^{2}) + (c^{2} – a^{2})

= a^{2} – b^{2} + b^{2} – c^{2} + c^{2} – a^{2}

= 0

= R.H.S

Hence, verified

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