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Question

Add.
(i) 9p + 16q ; 13p + 2q (ii) 2a + 6b + 8c; 16a + 13c+ 18b
(iii) 13x2-12y2 ; 6x2 - 8y2 (iv) 17a2 b2 + 16c ; 28c - 28a2 b2
(v) 3y2 - 10y + 16 ; 2y-7 ​ (vi) -3y2 + 10y -16 ; 7y2 + 8

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Solution


(i) (9p + 16q) + (13p + 2q)
= 9p + 16q + 13p + 2q
=(9p + 13p) + (16q + 2q)
=22p + 18q

(ii) (2a + 6b + 8c) + (16a + 13c + 18b)
= 2a + 6b + 8c + 16a + 13c + 18b
= (2a + 16a) + (6b + 18b) + (8c + 13c)
= 18a + 24b + 21c

(iii) (13x2 − 12y2) + (6x2 − 8y2)
= 13x2 − 12y2 + 6x2 − 8y2
= (13x2 + 6x2) + (−12y2 − 8y2)
=19x2 + (−20y2)
=19x2 − 20y2

(iv) (17a2b2 + 16c) + (28c − 28a2b2)
= 17a2b2 + 16c + 28c − 28a2b2
= (17a2b2 − 28a2b2) + (16c + 28c)
= −11a2b2 + 44c

(v) (3y2 − 10y + 16) + (2y − 7)
= 3y2 − 10y + 16 + 2y − 7
= 3y2 + (−10y + 2y) + (16 − 7)
=3y2 + (−8y) + 9
=3y2 − 8y + 9

(vi) (−3y2 + 10y − 16) + (7y2 + 8)
= −3y2 + 10y − 16 + 7y2 + 8
= (−3y2 + 7y2) + 10y + (−16 + 8)
= 4y2 + 10y + (−8)
= 4y2 + 10y − 8

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