Class 7 Algebraic Expressions Exercise 7.3

\begin{array}{l} \text {Q1. Place the last two terms of the following expressions in parentheses preceded by minus sign: } \\ \text {(i) } \quad x+y-3 z+y \quad \text {(ii) } \quad 3 x-2 y-5 z-4 \quad \text {(iii) } \quad 3 a-2 b+4 c-5 \\ \text {(iv) } \quad 7 a+3 b+2 c+4 \quad \text {(v) } \quad 2 a^{2}-b^{2}-3 a b+6 \quad \text {(vi) } \quad a^{2}+b^{2}-c^{2}+a b-3 a c \end{array}\begin{array}{l} \text {Sol. } \\\text {(i) } \quad x+y-3 z+y=x+y-(3 z-y) \\ \text {(ii) } \quad 3 x-2 y-5 z-4=3 x-2 y-(5 z+4) \\ \text {(iii) } \quad 3 a-2 b+4 c-5=3 a-2 b-(-4 c+5) \\ \text {(iv) } \quad 7 a+3 b+2 c+4=7 a+3 b-(-2 c-4) \\ \text {(v) } \quad 2 a^{2}-b^{2}-3 a b+6=2 a^{2}-b^{2}-(3 a b-6) \\ \text {(vi) } \quad a^{2}+b^{2}-c^{2}+a b-3 a c=a^{2}+b^{2}-c^{2}-(-a b+3 a c) \\\end{array}\begin{array}{l} \text {Q2. Write each of the following statements by using appropriate grouping symbols: } \\ \text {(i) The sum of } a-b \text { and } 3 a-2 b+5 \text { is subtracted from } 4 a+2 b-7 \\ \text {(ii) Three times the sum of } 2 x+y-\{5-(x-3 y)\} \text { and } 7 x-4 y+3 \text { is subtracted from } 3 x-4 y+7 \\ \text {(iii) The subtraction of } x^{2}-y^{2}+4 xy \text { from } 2 x^{2}+y^{2}-3 x y \text { is added to } 9 x^{2}-3 y^{2}-xy \end{array}\begin{array}{l} \text {Sol. } \\\text {(i) The sum of } a-b \text { and } 3 a-2 b+5 =(a-b)+(3 a-2 b+5) \\\text {The required expression } = (4 a+2 b-7)-[(a-b)+(3 a-2 b+5) ] \\ \\\text {(ii) Three times the sum of } 2 x+y-\{5-(x-3 y)\} \text { and } 7 x-4 y+3 \\ =3[(2 x+y-\{5-(x-3 y)\}) +(7 x-4 y+3)] \\\text {The required expression } = (3 x-4 y+7)-3[(2 x+y-\{5-(x-3 y)\})+(7 x-4 y+3)] \\ \\\text {(iii) The subtraction of } x^{2}-y^{2}+4 xy \text { from } 2 x^{2}+y^{2}-3 x y \\ =\{(2 x^{2}+y^{2}-3 x y)-(x^{2}-y^{2}+4 x y)\} \\ \text {The required expression } = \{(2 x^{2}+y^{2}-3 x y)-(x^{2}-y^{2}+4 x y)\}+(9 x^{2}-3 y^{2}-x y) \\\end{array}