New Learning Composite Mathematics SK Gupta Anubhuti Gangal Class 8 Algebraic Expressions Self Practice 5A Solution
(1) Answer whether each of the following expressions is a polynomial or not.
(a) 5x2 – 3x + 1
(b) 3√x – 5x – 11
(c) √3x3 + 8
(d) 2m-1 + m + 1
(e) 5x
(f) 59
(g) x/2 + 3
(h) 9/x – 2x2 + 13
(i) 3/2x+1
(j) πx2 – 2
(2) Identify each polynomial as a monomial, binomial, trinomial or as neither of these. Then give the coefficients of the polynomial and if the polynomial is in simple form, give its degree.
(a) 2p2 + 5p3 + p
(b) 7a2 + 5a + (-7)a4
(c) a2 – b2
(d) 8x5 + 3x3y – 2x2y2 + y6
(e) -18x6
(f) xy + yz + zx
(3) Pick out like terms in each polynomial.
(a) ab + ac + 3ab + 3ac
(b) 3xy + xz + 5xy – 7xz
(c) -8 + x2y + 5 + 3x2y
(d) ab + 2a2b2 + 4ab + 3a2b2
(e) xyz + x2yz3 + x3yz – xy3z2
(f) 23x2y + 25x2y – 32x2y + 26xy2
(4) Simplify:
(4) (a) 15b + 8b
(b) 7p – p + 21p – 8p
(c) 5x2+ 8x + 7 + 9x2 – 2x – 12
(d) 59 + 20y4 + 30y4
(e) (7x3 + 5x2 + 3x + 8) + (9x3 – 2x2 + 9 – 7x)
(5) Find the sum of the given polynomials.
(a) (3x + 4) + (7x – 1)
(b) (3y2 + 4y – 7) + (y2 + y + 12)
(c) (x4 – x2y + 3y2) + (-x4 + 2x2y + y2)
SOLUTION No. 1, 2, 3, 4 & 5:
(6) Subtract:
(a) (7y2 + 5x2) – (2y2 – 3x2)
(b) (5ab + 6bc – 7ca) – (-2ab + 4bc + 2ca)
(c) (4a – 3b – 9c) – (-2a – 5b – 10c)
SOLUTION No. 6:
(7) Find:
(a) The sum of the given polynomials.
(b) The difference of the given polynomials (2nd from the 1st).
(i) -5x + 9; 2x + 3
(ii) 7q + p; q – p
(iii) y4 – 9, y4 + 3
(iv) 5m2 + 3m + 8; 6m2 + 2m + 10
(v) x2 – xy – y2; -x2 + xy – y2
(vi) 3m2 – 5mn + 7n2; 2mn – 5n2 – m2
SOLUTION Number 7:
(8) Subtract the second polynomial from the first:
(a) 5m2 – 4n2; -5m2+ 6mn + 6n2
(b) a2 + 2ab – b2; 4a2 – 2ab + 4b2
Simplify
(9) (3x2 + 5x + 4) + (x2 + 6) – (3 – 7x)
(10) (x2 + y2 – z2) – (3z2 – 2x2 – 4y2) +(4y2 + x2 + z2)
SOLUTION Number 8, 9 & 10:
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