Identify the monomials, binomials, trinomialsand quadrinomials from the following expressions:
(i) a2
(ii) a2 − b2
(iii) x3 + y3+ z3
(iv) x3 + y3+z3 + 3xyz
(v) 7 + 5
(vi) a b c + 1
(vii) 3x – 2 + 5
(viii) 2x – 3y + 4
(ix) x y + y z + z x
(x) ax3 +bx2 + cx + d
Write all the terms of each of the following algebraic expressions:
(i) 3x
(ii) 2x – 3
(iii) 2×2 − 7
(iv)2×2 + y2− 3xy +4
Identify the terms and also mention the numerical coefficients of those terms:
(i) 4xy, -5x2y, -3yx, 2xy2
(ii) 7a2bc,-3ca2b, -(5/2)abc2, 3/2abc2, (-4/3)cba2
Identify the like terms in the following algebraic expressions:
(i) a2 + b2 -2a2 + c2 + 4a
(ii) 3x + 4xy − 2yz + 52zy
(iii) abc + ab2c+ 2acb2 + 3c2ab + b2ac − 2a2bc + 3cab2
Write the coefficient of x in thefollowing:
(i) –12x
(ii) –7xy
(iii) xyz
(iv) –7ax
Three numbers are in the ratio 2: 3: 5 and the sum of these numbers is 800. Find the numbers
Write the coefficient of x2 in the following:
(i) −3×2
(ii) 5x2yz
(iii) 5/7x2z
(iv) (-3/2) ax2 + yx
Write the coefficient of:
(i) y in –3y
(ii) a in 2ab
(iii) z in –7xyz
(iv) p in –3pqr
(v) y2 in 9xy2z
(vi) x3 in x3 +1
(vii) x2 in −x2
Write the numerical coefficient of each in the following:
(i) xy
(ii) -6yz
(iii) 7abc
(iv) -2x3y2z
Write the numericalcoefficient of each term in the followingalgebraic expressions:
(i)4x2y – (3/2)xy + 5/2 xy2
(ii) (–5/3)x2y+ (7/4)xyz + 3
Write the constant term of each of the following algebraic expressions:
(i) x2y− xy2 + 7xy − 3
(ii) a3− 3a2 + 7a + 5
Evaluate each of the following algebraic expressions for x = 1, y = -1, z = 2, a = -2, b = 1, c = -2:
(i) ax + by + cz
(ii) ax2 +by2 – cz
(iii) axy + byz + cxy
Add the following:
(i) 3x and 7x
(ii)-5xy and 9xy
Simplify the following algebraic expressions by removing grouping symbols.
2x + (5x – 3y)
Simplify each of the following:
(i) 7x3y +9yx3
(ii) 12a2b+ 3ba2
(i) 7abc, -5abc,9abc, -8abc
(ii) 2x2y,- 4x2y, 6x2y, -5x2y
(i) x3 -2x2y+ 3xy2- y3, 2×3- 5xy2 + 3x2y- 4y3
(ii) a4 – 2a3b+ 3ab3 + 4a2b2 + 3b4, – 2a4- 5ab3 + 7a3b – 6a2b2 + b4
Add the following expressions:
(i) 8a – 6ab +5b, –6a – ab – 8b and –4a + 2ab + 3b
(ii) 5×3+ 7 + 6x – 5×2, 2×2 – 8 – 9x, 4x – 2×2 + 3 x 3, 3 x 3 – 9x – x2 and x – x2 – x3 – 4
(i) x – 3y – 2z
5x + 7y – 8z
3x – 2y + 5z
(ii) 4ab – 5bc + 7ca
–3ab + 2bc – 3ca
5ab – 3bc + 4ca
Add x2 + 2xy + y2 to the sum of x2 – 3y2and 2×2 – y2 + 9.
Add a3+ b3 – 3 to the sum of 2a3 -3b3 – 3ab + 7 and -a3 + b3 + 3ab – 9.
Subtract:
(i) 7a2b from 3a2b
(ii) 4xy from -3xy
(i) – 4x from 3y
(ii) – 2x from – 5y
(i) 6×3 −7×2+ 5x − 3 from 4 − 5x + 6×2 − 8×3
(ii) − x2−3z from 5×2– y + z + 7
(iii) x3 +2x2y + 6xy2 − y3 from y3−3xy2−4x2y
From
(i) p3 – 4+ 3p2, take away 5p2 − 3p3 + p − 6
(ii) 7 + x − x2,take away 9 + x + 3×2 + 7×3
(iii) 1− 5y2,take away y3 + 7y2 + y +1
(iv) x3 −5×2 + 3x + 1, take away 6×2 − 4×3 + 5 + 3x
From the sum of 3×2 − 5x + 2 and − 5×2 − 8x +9 subtract 4×2 − 7x + 9.
Subtract the sum of13x – 4y + 7z and – 6z + 6x + 3y from the sum of 6x – 4y – 4z and 2x + 4y – 7.
What should be added to xy –3yz + 4zx to get 4xy – 3zx + 4yz + 7?
What should be subtracted from x2 – xy + y2 – x + y + 3 to obtain −x2 + 3y2 − 4xy + 1?
How much is x – 2y + 3z greater than 3x + 5y – 7?
How much is x2 − 2xy + 3y2 less than 2×2− 3y2 + xy?
How much does a2 − 3ab + 2b2 exceed 2a2 − 7ab + 9b2?
What must be added to 12×3 − 4×2 + 3x − 7 to make the sum x3 + 2×2 − 3x + 2?
If P = 7×2 + 5xy − 9y2, Q = 4y2 − 3×2 − 6xy and R = −4×2 + xy + 5y2, show that P + Q + R = 0.
If P = a2 − b2 + 2ab, Q = a2 + 4b2 −6ab, R = b2 + b, S = a2 − 4ab and T = −2a2 + b2– ab + a.
Find P + Q + R + S – T.
Place the last two terms ofthe following expressions in parentheses precededbya minus sign:
(i) x + y – 3z + y
(ii) 3x – 2y – 5z – 4
(iii) 3a – 2b + 4c – 5
(iv) 7a + 3b + 2c + 4 (v) 2a2 – b2 – 3ab+ 6
(vi)a2 + b2 – c2 + ab – 3ac
Write each of the following statements by using appropriate grouping symbols:
(i) The sum of a – b and 3a – 2b + 5 is subtracted from 4a + 2b – 7.
(ii) Three times the sum of 2x + y – [5 – (x – 3y)] and 7x – 4y + 3 is subtracted from 3x – 4y + 7
(iii) The subtraction of x2 – y2 + 4xyfrom 2×2 + y2 – 3xy is added to 9×2 – 3y2- xy.
5a – (3b – 2a + 4c)
-2(x2 – y2+ xy) – 3(x2 +y2 – xy)
3x + 2y – {x – (2y – 3)}
5a – {3a – (2 – a) + 4}
a – [b – {a – (b – 1) + 3a}]
a – [2b – {3a – (2b – 3c)}]
-x + [5y – {2x – (3y –5x)}]
2a – [4b – {4a – 3(2a –b)}]
-a – [a + {a + b – 2a – (a– 2b)} – b]
2x – 3y – [3x – 2y -{x – z– (x – 2y)}]
5 + [x – {2y – (6x + y – 4)+ 2x} – {x – (y – 2)}]
x2 – [3x + [2x -(x2 – 1)] + 2]
20 – [5xy + 3[x2- (xy – y) – (x – y)]]
85 – [12x – 7(8x – 3) –2{10x – 5(2 – 4x)}]
xy [yz – zx – {yx – (3y –xz) – (xy – zy)}]
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