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EXERCISE 12.1, , 1., , Get the algebraic expressions in the following cases using variables, constants and, , arithmetic operations,, (i) Subtraction of z from y., (ii) One-half of the sum of numbers x and y., (iii) | The number z multiplied by itself., (iv) — One-fourth of the product of numbers p and q., (v) Numbers x and y both squared and added., (vi) | Number 5 added to three times the product of numbers m and n., (vii) Product of numbers y and z subtracted from 10., (viii) Sum of numbers a and b subtracted from their product., Solution:, (i) The algebraic expression obtained by subtracting z from y is(y —z), (ii) Sum of numbers x and y is equal to x + y, One-half of the sum of numbers x and y is =, (iii) The algebraic expression obtained by multiplying number z by itself, = ZXL=2?, (iv) Product of numbers pand q is equal to p x q, One-fourth of product of numbers p and q is equal to om, (v) | Squared number of x is x?, Squared number of y is y?, Sum of squared numbers of x and y is equal to x? + y?, (vi) Product of numbers m and nis equal to mn, Three times the product of numbers m and n is equal to 3mn, The resulting expression after adding 5 to three times the product of, numbers m and n is equal to 5 + 3mn, (vii), , Product of numbers y and z is equal to yz
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The resulting expression after subtracting product of numbers y and z from, 10 is 10 — yz, , (viii) Sum of numbers a and b is equal to a + b, , Product of numbers a and b is equal to ab, , The resulting expression is ab — (a + b), , (i) Identify the terms and their factors in the following expressions, , Show the terms and factors by tree diagrams., , (a), (b), (c), (d), (ce), , x-3, Lt+x+x?, yoy, , 5xy? + 7x2y, —ab + 2b? — 3a?, , (ii) Identify terms and factors in the expressions given below:, , (a), (b), (c), (d), (e), (f), (g), (h), Solution:, , a @, , (b), , -4x4+5, , -4x + Sy, , 5y + 3y?, , xy + 2x? y?, , pq+q, , 1.2ab- 24b+3.6a, ae, , 0.1p? + 0.24?, , Terms of given expression are x, -3, , Tree diagram:, , x=3, , x -3, , Terms of given expression are 1, x, x”
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Factors of x? are x, x., , Tree diagram:, , ., 1+x +x", , _, », t, , (c) Terms of given expression are y, —y?, Factors of —y? are -1,y,y,y, Tree diagram:, , y-y, , , , (d) Terms in given expression are 5xy”, 7x?y, Factors of 5xy? are 5,x,y, yFactors of 7xy are 7,X,X,y, , Tree diagram:, , , , 5xy2 47327, 2 2, sp Tey, 5 ¢ 3 7 2, , (ec) Terms in given expression are —ab, 2b”, —3a?
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(ii), , (a), , (b), , (c), , (d), , (©), , (f), , (g), , Factors of —ab are —1, a,b., Factors of 2b? are 2, b, b., Factors of —3a? are —3,a,a., , Tree diagram:, , -ab +2b? -3a”, , , , Terms in given algebraic expression are —4x,5, Factors of —4x are —4, x, , Terms in algebraic expression —4x + Sy are —4x, 5y, Factors of —4x are —4, x, , Factors of Sy are 5,y, , Terms in given algebraic expression are 5y, 3y?, Factors of 5y are 5,y, , Factors of 3y? are 3, y,y, , Terms in given algebraic expression are xy, 2x*y”, Factors of xy are x, y, , Factors of 2x*y? are 2,x,x%,Y,y, , Terms in given algebraic expression are pq,q, , Factors of pq are p,q, , Terms in given algebraic expression are 1.2ab, —2.4b,3.6a, Factors of 1.2ab are 1.2,a,b, , Factors of —2.4b are —2.4,b, , Factors of 3.6a are 3.6, a., , Tems in given algebraic expression are 2x2
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3 3, Factors of 7x are 7,, , (h) Terms in given algebraic expression are 0.1p”, 0.2q?, Factors of 0.1p? are 0.1, p,p, Factors of 0.2q? are 0.2,q, 4, , Identify the numerical coefficients of terms (other than constants) in the following, , expressions:, , (@) 5-3?, , di) 14+ ¢t4+t? +03, , (iii) x+ 2xy+3y, , (iv) 100m + 1000n, , (vy) —p?q? + 7pq, , (vi) 12a+08b, , (vii) 3.147?, , (viii) 2(1+ b), , (ix) O01 y+0.01 y?, , Solution:, , (i) The term other than constant is —3¢*, Numerical coefficient of term —3t? = —3, , (ii) The terms other than constant are t, t?and t?, Numerical coefficient of t is equal to 1, Numerical coefficient of t? is equal to 1, Numerical coefficient of t? is equal to 1, , (iii) | The terms other than constant are x, 2xy, 3y, Numerical coefficient of x is equal to 1, Numerical coefficient of 2xy is equal to 2, Numerical coefficient of 3y is equal to 3, , (iv) The terms other than constant are 100m and 1000n, , Numerical coefficient of 100m is equal to 100, Numerical coefficient of 1000n is equal to 1000.
