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Question -

(a) Add: p(p – q), q(q – r) and r(r – p)
(b) Add: 2x(z – x – y) and 2y(z – y – x)
(c) Subtract: 3l(l – 4m + 5n) from 4l(10n – 3m + 2l)
(d) Subtract: 3a(a + b + c) – 2b(a – b + c) from 4c(-a + b + c)



Answer -

(a) p(p – q) + q(q – r) + r(r – p)
= (p × p) – (p × q) + (q × q) – (q × r) + (r × r) – (r × p)
= p2 –pq + q2 –qr + r2 –rp
= p2 +q2 +r2 –pq – qr – rp
(b) 2x(z – x – y) + 2y(z – y – x)
= (2x × z) – (2x × x) – (2x × y) + (2y × z) – (2y × y) – (2y × x)
= 2xz – 2x2 –2xy + 2yz – 2y2 –2xy
= -2x2 –2y2 +2xz + 2yz – 4xy
= -2x2 –2y2 –4xy + 2yz + 2xz
(c) 4l(10n – 3m + 2l) – 3l(l – 4m + 5n)
= (4l × 10n) – (4l × 3m) + (4l × 2l) – (3l × l) – (3l × -4m) – (3l × 5n)
= 40ln – 12lm + 8l2 –3l2 +12lm – 15ln
= (40ln – 15ln) + (-12lm + 12lm) + (8l2 –3l2)
= 25ln + 0 + 5l2
= 25ln + 5l2
= 5l2 +25ln
(d) [4c(-a + b + c)] – [3a(a + b + c) – 2b(a – b + c)]
= (-4ac + 4bc + 4c2) – (3a2 +3ab + 3ac – 2ab + 2b2 –2bc)
= -4ac + 4bc + 4c2 –3a2 –3ab – 3ac + 2ab – 2b2 +2bc
= -3a2 –2b2 +4c2 –ab + 6bc – 7ac

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