Page 164 - classs 6 a_Neat

EXAMPIE:16 Simplify: (x - y + 2xy + 1) - (x + y + 4xy - 5) 5. Write the number of terms in each algebraic expression and then identify them
2
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2
SOLUTION Here, a '-' sign precedes the second parenthesis, so we remove it and change the sign as monimial, binomial, trinomial or polynomial.
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of each term within. a.p + 2pq + q b.x -y c.8m
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(x -y +2xy+l) - (x +y +4xy-5) d.a + b +c + 2ab + 2bc + 2ca e.p × q × r
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= x -y +2xy +1 -x - y -4xy + 5 6. Separate the like terms from the unlike terms.
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= (1 - l)x -2y +(2 - 4)xy + 6 a.x , x y, 3x , 7yx , zyx
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∴ = - 2y - 2xy + 6. b.10pq, 10q, 10p, 10, 7pq
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EXAMPIE:17 Simplify: 2x - [3y -{2x - (y - x)}] c.m, -n, m , n , 14m n 2
SOLUTION We first remove the innermost grouping symbol ( ), then { }, and then I ]. Thus, we d.pqr, 1 Spqr, -?qr, 8pq, 9pr
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have: e.a , b , c , a + b + c , 7b , -c , 1 0a 2
2x - [3y -{2x - (y - x)}] 7. Complete the table.
= 2x - [3y - {2x - y + x}] Number of Kind of Algebraic Factors of each
= 2x - [3y -{3x - y}] Algebraic Expression Terms Expression Term
= 2x - (3y-3x +yl
2
= 2x - [4y - 3x ] a.x + y 2
= 2x - 4y + 3x b.ax+ by+ cz
= 5x - 4y.
EXAMPIE:18 Simplify: 2a -[3b -{a -(2e -3b) + 4e -3(a -b -2e)}]
SOLUTION We first remove the innermost grouping symbol ( ), then { }, and then [ ]. Thus, we c.8pqr
have:
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2
2
2a - [3b - {a - (2e - 3b) + 4e - 3(a - b - 2e)}] d.a +b +c +d 2
= 2a - [3b -{a - 2e + 3b + 4e - 3a + 3b + 6c}]
= 2a - [3b -{- 2a + 6b +Be} ] e.m -2mn + n 2
2
= 2a - [3b + 2a - 6b - Be]
= 2a - [-3b + 2a - Be]
= 2a + 3b - 2a + Be 8. Pick the like terms and add them.
= 3b + Be. a. pq, 7pq, -1 0pq, pqr b. x2, 4x2, 7x2y c. a, 1 Sa, 20abc, 12a2
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JUST TRY:1 Rad ha has ₹60 in her piggy bank and Sadhana gives her ₹x. The total amount d. Sxyz, 10x yz, 1Sxy z, 25xyz , 30xyz e m 3m - 7m 8m Sn 2
of money that Rad ha now has is ₹100. How much money did Sadhana give Rad ha? 9. Write the following statements as algebraic expressions.
JUST TRY:2 The perimeter of a square is 120 m. Find the side of the square. a.One pencil costs <5 and a pen costs <10. Write the total cost if Rajeev buys x pencils and y pens.
JUST TRY:3 7x + y b.Sana is 2 years older than her sister Sania. Write Sana's age if Sania is p years old.
JUST TRY:4 3x + 2x-5 c.Sameer thinks of a number, adds 27 to it and then divides it by 10.
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JUST TRY:5 7xy + 2xz + Syz EXERCISE-11 e.Aman is x years old now. Write his age 7 years from now and 7 years ago. Also write the expression
for his mother’s age who will be 3 times older than Aman after 7 years.
1 . Write the following as algebraic expressions. 10. Find the value of the given algebraic expressions.
a. Seven times y. b. 6 plus x. a. a+ b + c if a = 5, b = 7, c = 9
c. x plus 2x minus 6. d. x plus y is equal to 2. b. pq + qr +rp if p =2, q = 5, r = 3
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e. 10 times x plus 4 times y. f.a is 7 more than b. c. m - n 2 if m = 5, n = 4
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g.a is 9 less than c. h.One-fourth of a number x minus 8. d. a - 12ab + 9b if a = 1, b = 2
x= 1, y = 0, z = -1
e. x +y +z + 3xyz if
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i.The square oft plus 10. j. a plus b minus c multiplied by d
2. Write the following algebraic expressions in words. 1. Arun a went to the market with ₹p. She bought an item A for ₹a and item B for ₹b. Express the
a.x + 7 b.2x -3 c. y + 1 2. amount left with her.
How many minutes are equal to 5 seconds? Solve using algebra.
3 3. The number of bacteria in a culture is x today. It becomes double of itself after one week. What will be

d. a bc+− e.(10a + b)c its number after three weeks?
d
3. Write the numerical coefficients of the following algebraic expressions.
a.1 0x 2 b.7xy C.x d.2a b e. 9mn
2 2
4. Write the coefficient of x in the following algebraic expressions.
a. 25xy b.7y + 3x C.p + q +2px d.-10x + y e.9xy + 19xy 2
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