অনুশীলনী – 9(B)
1. যোগ কৰা ——
(i) -4a , -7a, 9a
Solution:-
= -(4a) + (-7a) + 9a
= – 4a – 7a + 9a
= – 11a + 9a = 2a
(ii) 12c\(d^2\) , -5c\(d^2\), -7c\(d^2\)
Solution:-
= 12c\(d^2\) +( -5c\(d^2\)) + (-7c\(d^2\))
= 12c\(d^2\) – 5c\(d^2\) – 7c\(d^2\)
= 12c\(d^2\) – 12c\(d^2\)
= 0
(iii) -10\(x^2\) , 12\(x^2\), -8x , – 3x
Solution:-
= -10\(x^2\) + 12\(x^2\) + (-8x) +(- 3x)
= -10\(x^2\) + 12\(x^2\) -8x – 3x
= 2\(x^2\) – 11x
(iv) \(axy , bxy , cxy\)
Solution:-
= \(axy + bxy + cxy\)
= x(\(ay + bxy + cxy\))
(v) \(4a^2\ – 5ab\ -6b^2\ ; 10ab\ – 6a^2\ – 8b^2\) আৰু \(10b^2 -3a^2 -7ab\)
Solution:-
= \(4a^2\ – 5ab\ -6b^2\ + 10ab\ – 6a^2\ – 8b^2\) + \(10b^2 -3a^2 -7ab\)
= \(-5a^2\ – 2ab\ -4b^2\)
(vi) \(9x^2\ – 4xy\ -7y^2\ ; -5xy\ +6y^2\ – 3x^2\) আৰু \(11y^2 +7xy -5x^2\)
Solution:-
= \(9x^2\ – 4xy\ -7y^2\ + (-5xy)\ +6y^2\ – 3x^2\) + \(11y^2 +7xy -5x^2\)
= \(9x^2\ – 4xy\ -7y^2\ -5xy)\ +6y^2\ – 3x^2\) + \(11y^2 +7xy -5x^2\)
= \(x^2\ – 2xy\ +24y^2\)
(vii) \(\frac{5}{9}abc\ + \frac{2}{7}a^2bc+ \frac{2}{7}ab^2c + 1\) আৰু \(\frac{2}{3 }ab^2c – \frac{7}{2}abc+ \frac{8}{3}\)
Solution:-
= \(\frac{5}{9}abc\ + \frac{2}{7}a^2bc+ \frac{2}{7}ab^2c + 1\) + \(\frac{2}{3 }ab^2c – \frac{7}{2}abc+ \frac{8}{3}\)
= \(\frac{5}{9}abc\ – \frac{7}{2}abc+ \frac{2}{7}ab^2c +\frac{2}{3 }ab^2c + 1+\frac{8}{3}\)
= \(\frac{10-63}{18}abc\ + \frac{6+14}{21}ab^2c +\frac{3+8}{3}\)
= \(\frac{-53}{18}abc\ + \frac{20}{21}ab^2c +\frac{11}{3}\)
2. প্ৰথম ৰাশিৰ পৰা দ্ধিতীয় ৰাশি বিয়োগ কৰা ——
(i) \(-15pq, – 10pq\)
Solution:-
= \((-10pq)-(-15pq)\)
= \(-10pq +15pq\)
= \(5pq\)
(ii) \(x^2 -3x, \; -2x^2- 4x\)
Solution:-
= \((-2x^2- 4x)-(x^2-3x)\)
= \(-2x^2- 4x – x^2+3x\)
= \(-3x^2 – x\)
(iii) \(4a^3x^2 – 3ax^4 + a^5\ ; 3a^3x^2 + 7a^2x^3 – a^5\)
Solution:-
= \((3a^3x^2 + 7a^2x^3 – a^5)\ – (4a^3x^2 – 3ax^4 + a^5)\)
= \(3a^3x^2 + 7a^2x^3 – a^5\ – 4a^3x^2 + 3ax^4 – a^5)\)
= \(-a^3x^2 + 7a^2x^3 – 2a^5 + 3ax^4\)
(iv) \(19 – 3x – 15y + 7xy – 2xy^2\ + 3x^2y ; \; 6x^2y – 4xy +7xy^2 – 8x + 9y -11\)
Soloution:-
= \(19 – 3x – 15y + 7xy – 2xy^2\ + 3x^2y\ + 6x^2y – 4xy +7xy^2 – 8x + 9y -11\)
= \(8 – 11x – 6y + 3xy + 5xy^2 + 9x^2y\)
(v) \(\frac{1}{5}x^3\ – \frac{3}{2}x^2+ \frac{2}{3}x + \frac{1}{4}\) ; \(\frac{8}{5}x^2 – \frac{2}{3}x^3+ \frac{3}{2}x – 1\)
Solution:-
= (\(\frac{1}{5}x^3\ – \frac{3}{2}x^2+ \frac{2}{3}x + \frac{1}{4}\)) – (\(\frac{8}{5}x^2 – \frac{2}{3}x^3+ \frac{3}{2}x – 1\))
= \(\frac{1}{5}x^3 + \frac{2}{3}x^3 – \frac{3}{2}x^2 – \frac{8}{5}x^2 + \frac{2}{3}x – \frac{3}{2}x + \frac{1}{4} +1\)
= \(\frac{9 -10}{15}x^3 – \frac{15+16}{10}x^2 + \frac{4-9}{6}x + \frac{1+4}{4}\)
= \(\frac{-1}{15}x^3 – \frac{31}{10}x^2 + \frac{-5}{6}x + \frac{5}{4}\)
= \(\frac{-1}{15}x^3 – \frac{31}{10}x^2 – \frac{5}{6}x + \frac{5}{4}\)
(vi) \(3a^2\ – \frac{4}{3}a+ \frac{5}{3} ;\frac{-7}{3}a^2 – \frac{9}{4}a – 5\)
Solution:-
= \(\frac{-7}{3}a^2 – \frac{9}{4}a – 5\) – (\(3a^2\ – \frac{4}{3}a+ \frac{5}{3}\))
= \(\frac{-7}{3}a^2 – \frac{9}{4}a – 5\) – \(3a^2\ + \frac{4}{3}a – \frac{5}{3}\)
= \(\frac{-7}{3}a^2 – 3a^2 – \frac{9}{4}a + \frac{4}{3}a – \frac{5}{3} – 5\)
= \(\frac{-7}{3}a^2 – 3a^2 – \frac{9}{4}a + \frac{4}{3}a – \frac{5}{3} – 5\)