Question

Add the following:
(i) ab – bc, bc – ca, ca – ab
(ii) a – b + ab, b – c + bc, c – a + ac
(iii) 2p2q2 – 3pq + 4, 5 + 7pq – 3p2q2
(iv) l2 + m2, m2 + n2, n2 + l2, 2lm + 2mn + 2nl
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Answer 1

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(i) (ab-ab) + (-bc+bc) + (-ca + ca)

= 0+0+0

= 0

(ii) refer the attachment

(iii)( 2p^2q^2 - 3p^2q^2 ) + (-3pq + 7pq) + (4+5)

= -p^2q^2 + 4pq + 9

(iv)(12+12) +(m^2 + m^2) +(n^2 + n^2) + 2lm + 2mn + 2nl

= 24 + m^4 + n^4 + 2lm + 2mn + 2nl

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Answer 2

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$\huge{\underline{\mathfrak \purple{Answers}}}$

(i)

Given are 3 terms i.e.,

=>ab − bc + bc − ca + ca − ab

=>ab − ba + bc − bc + ca − ca

=>0

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(ii)

Three terms i.e,

=>a − b + ab + b − c + bc + c − a + ac

=>a − a + b − b + c − c + ab + bc + ca

=>ab + bc + ac

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(iii)

Adding the given two terms,

=>2p²q² - 3pq - 4 + 5 + 7pq - 3p²q²

=>2p²q² - 3pq²q² + 7pq - 3pq + 5 + 4

=>-p²q² + 4pq + 9

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(iv)

Addition of the four terms results in

=>l² + m² + n² + m² + l² + n² + 2lm + 2mn + 2nl

=>2l² + 2m² + 2n² + 2(lm + mn + nl)

=>2(l² + m² + n² + lm + mn + nl)

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