question_answer 1)

                Find and correct the errors in the following mathematical statements. 1.            \[4(x-5)\,=4x-5\] 2.            \[x(3x+2)\,=3{{x}^{2}}+2\] 3.            \[2x+3y=5xy\] 4.            \[x+2x+3x=5x\] 5.            \[5y+2y+y-7y=0\] 6.            \[3x+2x=5{{x}^{2}}\] 7.            \[{{(2x)}^{2}}+4(2x)+7=2{{x}^{2}}+8x+7\] 8.            \[{{(2x)}^{2}}+5x=4x+5x=9x\] 9.            \[{{(3x+2)}^{2}}=3{{x}^{2}}+6x+4\]. 10.          Substituting \[x=-3\] in (a) \[{{x}^{2}}+5x+4\] gives \[{{(-3)}^{2}}\,+5(-3)\,+4\] \[=9+2+4=15\] (b) \[{{x}^{2}}-5x+4\] gives \[{{(-3)}^{2}}-5(-3)+4\] \[=9-15+4=-2\] (c) \[{{x}^{2}}+5x\] gives \[{{(-3)}^{2}}\,+5(-3)\] \[=-9-15=-24\]. 11.          \[{{(y-3)}^{2}}={{y}^{2}}-9\] 12.          \[{{(z+5)}^{2}}={{z}^{2}}+25\] 13.          \[(2a+3b)\,(a-b)\,=2{{a}^{2}}-3{{b}^{2}}\] 14.          \[(a+4)\,(a+2)\,={{a}^{2}}+8\] 15.          \[(a-4)\,(a-2)\,={{a}^{2}}-8\] 16.          \[\frac{3{{x}^{2}}}{3{{x}^{2}}}=0\] 17.          \[\frac{3{{x}^{2}}+1}{3{{x}^{2}}}=1+1=2\] 18.          \[\frac{3x}{3x+2}\,=\frac{1}{2}\] 19.          \[\frac{3}{4x+3}\,=\frac{1}{4x}\] 20.          \[\frac{4x+5}{4x}=5\] 21.          \[\frac{7x+5}{5}=7x\]

Answer:

1.            \[4(x-5)=4x-20\] 2.            \[x(3x+2)\,=3{{x}^{2}}+2x\] 3.            \[2x+3y=2x+3y\] 4.            \[x+2x+3x=6x\] 5.            \[5y+2y+y-7y=y\] 6.            \[3x+2x=5x\] 7.            \[{{(2x)}^{2}}+4(2x)\,+7=4{{x}^{2}}+8x+7\] 8.            \[{{(2x)}^{2}}+5x=4{{x}^{2}}+5x\] 9.            \[{{(3x+2)}^{2}}=9{{x}^{2}}+12x+4\]. 10.          (a) \[{{x}^{2}}+5x+4={{(-3)}^{2}}+5(-3)+4\] \[=9-15+4\] \[=-2\] and not 15 (b) \[{{x}^{2}}-5x+4\,={{(-3)}^{2}}-5(-3)+4\] \[=9+15+4\] = 28 and not ? 2 (c) \[{{x}^{2}}+5x={{(-3)}^{2}}+5(-3)\]                 \[=915\] \[=-6\] and not \[915=-24\] 11.          \[{{(y-3)}^{2}}={{y}^{2}}-2(y)\,(3)+{{(3)}^{2}}\] \[={{y}^{2}}-6y+9\] and not equal to \[{{y}^{2}}-9\] 12.          \[{{(z+5)}^{2}}={{z}^{2}}+2(z)\,(5)+{{(5)}^{2}}\] \[={{z}^{2}}+10z+25\] and not equal to \[{{z}^{2}}+25\] 13.          \[(2a+3b)\,(a-b)\] \[=2a(a-b)\,+3b(a-b)\] \[=2{{a}^{2}}-2ab+3ba-3{{b}^{2}}\] \[=2{{a}^{2}}+ab-3{{b}^{2}}\] and not equal to \[2{{a}^{2}}-3{{b}^{2}}\] 14.          \[(a+4)\,(a+2)\,=a\,(a+2)\,+4(a+2)\]\[\,={{a}^{2}}+2a+4a+8\] \[={{a}^{2}}+6a+8\] and not equal to \[{{a}^{2}}+8\]. 15.          \[(a-4)\,(a-2)=a(a-2)\,-4(a-2)\] \[={{a}^{2}}-2a-4a+8\] \[={{a}^{2}}-6a+8\] and not equal to \[{{a}^{2}}-8\] 16.          \[\frac{3{{x}^{2}}}{3{{x}^{2}}}=1\] and not equal to 0 17.          \[\frac{3{{x}^{2}}+1}{3{{x}^{2}}}\,=\frac{3{{x}^{2}}}{3{{x}^{2}}}\,+\frac{1}{3{{x}^{2}}}\] \[=1+\frac{1}{3{{x}^{2}}}\,\] and not equal to \[1+1=2\] 18.          \[\frac{3x}{3x+2}\,=\frac{3x}{3x+2}\] and not equal to \[\frac{1}{2}\] 19.          \[\frac{3}{4x+3}\,=\frac{3}{4x+3}\] and not equal to \[\frac{1}{4x}\] 20.          \[\frac{4x+5}{4x}=\frac{4x}{4x}\,+\frac{5}{4x}=1+\frac{5}{4x}\] and not equal to 5 21.          \[\frac{7x+5}{5}=\frac{7x}{5}+\frac{5}{5}\,=\frac{7x}{5}+1\] and not equal to \[7x\].