NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions (EX 12.3) Exercise 12.3

Q.1

$\begin{array}{l}\mathrm{If}\mathrm{m}=2,\mathrm{find}\mathrm{the}\mathrm{value}\mathrm{of}:\\ \left(\mathrm{i}\right)\mathrm{m}–2\left(\mathrm{ii}\right)3\mathrm{m}–5\left(\mathrm{iii}\right)9–5\mathrm{m}\\ \left(\mathrm{iv}\right)3{\mathrm{m}}^2–2\mathrm{m}–7\left(\mathrm{v}\right)\frac{5\mathrm{m}}{2}–4\end{array}$

Ans

$\begin{array}{l}\mathrm{Form}=2\\ \left(\mathrm{i}\right)\mathrm{m}-2\\ =2-2\\ =0\\ \left(\mathrm{ii}\right)3\mathrm{m}-5\\ =3\left(2\right)-5\\ =6-5=1\\ \left(\mathrm{iii}\right)9-5\mathrm{m}\\ =9–5\left(2\right)\\ =9-10=-1\\ \left(\mathrm{iv}\right)3{\mathrm{m}}^2-2\mathrm{m}-7\\ =3{\left(2\right)}^2-2\left(2\right)-7\\ =12-4-7=1\end{array}$

$\begin{array}{l}\left(\mathrm{v}\right)\frac{5\mathrm{m}}{2}-4\\ =\frac{5\left(2\right)}{2}-4\\ =\frac{10}{2}-4\\ =5-4=1\end{array}$

Q.2

$\begin{array}{l}\mathrm{If}\mathrm{p}=–2,\mathrm{find}\mathrm{the}\mathrm{value}\mathrm{of}:\\ \left(\mathrm{i}\right)4\mathrm{p}+7\left(\mathrm{ii}\right)–3{\mathrm{p}}^2+4\mathrm{p}+7\left(\mathrm{iii}\right)–2{\mathrm{p}}^3–3{\mathrm{p}}^2+4\mathrm{p}+7\end{array}$

Ans

$\begin{array}{l}\mathrm{For}\mathrm{p}=-2,\\ \left(\mathrm{i}\right)4\mathrm{p}+7\\ =4(-2)+7\\ =-8+7=-1\\ \left(\mathrm{ii}\right)-3{\mathrm{p}}^2+4\mathrm{p}+7\\ =-3{(-2)}^2+4(-2)+7\\ =-3\left(4\right)-8+7\\ =-12-1=-13\end{array}$

$\begin{array}{l}\left(\mathrm{iii}\right)-2{\mathrm{p}}^3-3{\mathrm{p}}^2+4\mathrm{p}+7\\ =-2{(-2)}^3-3{(-2)}^2+4(-2)+7\\ =-2(-8)-3\left(4\right)-8+7\\ =16-12-1\\ =3\end{array}$

Q.3

$\begin{array}{l}\mathrm{Find}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{the}\mathrm{following}\mathrm{expressions},\mathrm{when}\mathrm{x}=–1:\\ \left(\mathrm{i}\right)2\mathrm{x}–7\left(\mathrm{ii}\right)–\mathrm{x}+2\left(\mathrm{iii}\right){\mathrm{x}}^2+2\mathrm{x}+1\\ \left(\mathrm{iv}\right)2{\mathrm{x}}^2–\mathrm{x}–2\end{array}$

Ans

$\begin{array}{l}\mathrm{For}\mathrm{x}=-1:\\ \left(\mathrm{i}\right)2\mathrm{x}-7\\ =2(-1)-7\\ =-2-7=-9\\ \left(\mathrm{ii}\right)-\mathrm{x}+2\\ =-(-1)+2\\ =1+2=3\\ \left(\mathrm{iii}\right){\mathrm{x}}^2+2\mathrm{x}+1\\ ={(-1)}^2+2(-1)+1\\ =1-2+1=0\end{array}$

$\begin{array}{l}\left(\mathrm{iv}\right)2{\mathrm{x}}^2-\mathrm{x}-2\\ =2{(-1)}^2-(-1)-2\\ =2+1-2=1\end{array}$

Q.4

$\begin{array}{l}\mathrm{If}\mathrm{a}=2,\mathrm{b}=–2,\mathrm{find}\mathrm{the}\mathrm{value}\mathrm{of}:\\ \left(\mathrm{i}\right){\mathrm{a}}^2+{\mathrm{b}}^2\left(\mathrm{ii}\right){\mathrm{a}}^2+\mathrm{ab}+{\mathrm{b}}^2\left(\mathrm{iii}\right){\mathrm{a}}^2–{\mathrm{b}}^2\end{array}$

Ans

\begin{array}{l}Fora=2,b=-2,\\ \left(i\right)a^2+b^2\\ ={\left(2\right)}^2+{\left(-2\right)}^2\\ =4+4=8\\ \left(ii\right)a^2+ab+b^2\\ ={\left(2\right)}^2+2\left(-2\right)+{\left(-2\right)}^2\\ =4-4+4=4\\ \left(iii\right)a^2-b^2\\ ={\left(2\right)}^2-{\left(-2\right)}^2\\ =4-4=0\end{array}

Q.5

$\begin{array}{l}\mathrm{When}\mathrm{a}=0,\mathrm{b}=–1,\mathrm{find}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{expressions}:\\ \left(\mathrm{i}\right)2\mathrm{a}+2\mathrm{b}\left(\mathrm{ii}\right)2{\mathrm{a}}^2+{\mathrm{b}}^2+1\\ \left(\mathrm{iii}\right)2{\mathrm{a}}^2\mathrm{b}+2{\mathrm{ab}}^2+\mathrm{ab}\left(\mathrm{iv}\right){\mathrm{a}}^2+\mathrm{ab}+2\end{array}$

Ans

\begin{array}{l}Fora=0,b=-1,\\ \left(i\right)2a+2b\\ =2\left(0\right)+2\left(-1\right)\\ =0-2=-2\\ \left(ii\right)2a^2+b^2+1\\ =2{\left(0\right)}^2+{\left(-1\right)}^2+1\\ =0+1+1=2\\ \left(iii\right)2a^{2}b+2a{b}^2+ab\\ =2{\left(0\right)}^2\left(-1\right)+2\left(0\right){\left(-1\right)}^2+0\left(-1\right)\\ =0+0+0=0\\ \left(iv\right)a^2+ab+2\\ ={\left(0\right)}^2+\left(0\right)\left(-1\right)+2\\ =0+0+2=2\end{array}

Q.6

$\begin{array}{l}\mathrm{Simplify}\mathrm{the}\mathrm{expressions}\mathrm{and}\mathrm{find}\mathrm{the}\mathrm{value}\mathrm{if}\mathrm{x}\mathrm{is}\mathrm{equal}\mathrm{to}2\\ \left(\mathrm{i}\right)\mathrm{x}+7+4(\mathrm{x}–5)\left(\mathrm{ii}\right)3(\mathrm{x}+2)+5\mathrm{x}–7\\ \left(\mathrm{iii}\right)6\mathrm{x}+5(\mathrm{x}–2)\left(\mathrm{iv}\right)4(2\mathrm{x}–1)+3\mathrm{x}+11\end{array}$

Ans

$\begin{array}{l}\left(i\right)x+7+4(x-5)\\ =x+7+4x-20\\ =5x-13\\ Forx=2\\ 5x-13\\ =5\left(2\right)-13\\ =10-13=-3\\ \left(ii\right)3(x+2)+5x-7\\ 3x+6+5x-7\\ =8x-1\\ Forx=2\\ =8\left(2\right)-1\\ =16-1=15\\ \left(iii\right)6x+5(x-2)\\ =6x+5x-10\\ =11x-10\end{array}$

\begin{array}{l}Forx=2\\ =11\left(2\right)-10\\ =22-10=12\\ \left(iv\right)4(2x-1)+3x+11\\ =8x-4+3x+11\\ =11x+7\\ Forx=2\\ =11\left(2\right)+7\\ =22+7=29\end{array}

Q.7

$\begin{array}{l}\mathrm{Simplify}\mathrm{these}\mathrm{expressions}\mathrm{and}\mathrm{find}\mathrm{their}\mathrm{values}\mathrm{if}\mathrm{x}=3,\\ \mathrm{a}=–1,\mathrm{b}=–2.\\ \left(\mathrm{i}\right)3\mathrm{x}–5–\mathrm{x}+9\left(\mathrm{ii}\right)2–8\mathrm{x}+4\mathrm{x}+4\\ \left(\mathrm{iii}\right)3\mathrm{a}+5–8\mathrm{a}+1\left(\mathrm{iv}\right)10–3\mathrm{b}–4–5\mathrm{b}\\ \left(\mathrm{v}\right)2\mathrm{a}–2\mathrm{b}–4–5+\mathrm{a}\end{array}$

Ans

\begin{array}{l}\left(i\right)3x-5-x+9\\ =3x-x-5+9\\ =2x+4\\ Forx=3,a=-1,b=-2\end{array}

\begin{array}{l}2x+4\\ =2\left(3\right)+4\\ =6+4=10\\ \left(ii\right)2-8x+4x+4\\ =-4x+6\\ Forx=3,a=-1,b=-2\\ -4x+6\\ =-4\left(3\right)+6\\ =-12+6=-6\\ \left(iii\right)3a+5-8a+1\\ =-5a+6\\ Forx=3,a=-1,b=-2\\ -5a+6\\ =-5\left(-1\right)+6\\ =5+6=11\\ \left(iv\right)10-3b-4-5b\\ =10-4-3b-5b\\ =6-8b\\ Forx=3,a=-1,b=-2\\ 6-8b=6-8\left(-2\right)\\ =6+16=22\\ \left(v\right)2a-2b-4-5+a\\ =3a-2b-9\\ =3\left(-1\right)-2\left(-2\right)-9\\ =-3+4-9\\ =-8\end{array}

Q.8

$\begin{array}{l}\left(\mathrm{i}\right)\mathrm{If}\mathrm{z}=10,\mathrm{find}\mathrm{the}\mathrm{value}\mathrm{of}{\mathrm{z}}^3–3(\mathrm{z}–10).\\ \left(\mathrm{ii}\right)\mathrm{If}\mathrm{p}=–10,\mathrm{find}\mathrm{the}\mathrm{value}\mathrm{of}{\mathrm{p}}^2–2\mathrm{p}–100.\end{array}$

Ans

\begin{array}{l}\left(i\right)Forz=10,\\ z^3–3(z–10)\\ ={\left(10\right)}^3-3\left(10-10\right)\\ =1000-3\left(0\right)=1000\\ \left(ii\right)Forp=-10,\\ p^2-2p-100\\ ={\left(-10\right)}^2-2\left(-10\right)-100\\ =100+20-100\\ =20\end{array}

Q.9 What should be the value of a if the value of 2x² +x – a equals to 5, when x = 0?

Ans

\begin{array}{l}Given,2x^2+x-a=5,whenx=0\\ So,plugx=0toget\\ 2{\left(0\right)}^2+0-a=5\\ 0+0-a=5\\ -a=5\\ a=-5\end{array}

Q.10

$\begin{array}{l}\mathrm{Simplify}\mathrm{the}\mathrm{expression}\mathrm{and}\mathrm{find}\mathrm{its}\mathrm{value}\mathrm{when}\mathrm{a}=\; 5\mathrm{and}\\ \mathrm{b}=\; –3.\\ \mathrm{2(}{\mathrm{a}}^{\mathrm{2}}+\mathrm{ab})+3–\mathrm{ab}\end{array}$

Ans

\begin{array}{l}\text{Simplifying to get}\\ 2(a^2+ab)+3-ab\\ =2a^2+2ab+3-ab\\ =2a^2+ab+3\end{array}

\begin{array}{l}whena=5andb=-3,\\ 2{\left(5\right)}^2+5\left(-3\right)+3\\ =50-15+3\\ =53-15\\ =38\end{array}