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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 â€‹ (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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