question_answer 1)

                (a) Add: \[p(p-q),\,q(q-r)\] and \[r(r-p)\]                 (b) Add: \[2x(z-x-y)\] and \[2y(z-y-x)\]                 (c) Subtract: \[3l(l-4m+5n)\] from \[(10n-3m+2l)\] (d) Subtract: \[3a(a+b+c)\,-2b(a-b+c)\] from \[4c(-a+b+c)\].

Answer:

                (a) First expression \[=p(p-q)\,=p\times p-p\times q\] \[={{p}^{2}}-pq\] Second expression                 \[=q(q-r)\] \[=q\times q-q\times r\] \[={{q}^{2}}-qr\]                 Third expression \[=r(r-p)\] \[=r\times r-r\times p\] \[={{r}^{2}}-rp\]                 Adding the three expressions,

	\[{{p}^{2}}-pq\]
+		\[+{{q}^{2}}-qr\]
+			\[+{{r}^{2}}-rp\]
\[{{p}^{2}}-pq+{{q}^{2}}-qr+{{r}^{2}}-rp\]

                (b) First expression \[=2x(z-x-y)\] \[=(2x)\times (z)-(2x)\,\times (x)-(2x)\times (y)\] \[=2xz-2{{x}^{2}}-2xy\] Second expression \[=2y(z-y-x)\] \[=(2y)\times (z)-(2y)\times (y)-(2y)\times (x)\] \[=2yz-2{{y}^{2}}-2yx\] Adding the two expressions,

	\[2xz-2{{x}^{2}}-2xy\]
+	\[-2yx+2yz-2{{y}^{2}}\]
\[2xz-2{{x}^{2}}-4xy+2yz-2{{y}^{2}}\]

(c) First expression \[=3l\,(l-4m+5n)\] \[=(3l)\times (l)-(3l)\times (4m)+(3l)\times (5n)\] \[=3{{l}^{2}}-12lm+15\ln \] Second expression \[=4l\,(10n-3m+2l)\] \[=(4l)\times (10n)-(4l)\times (3m)+(4l)\times (2l)\] \[=40\,\ln -12lm\,+8{{l}^{2}}\] Subtraction \[\to \]

\[40\ln -12lm+8{{l}^{2}}\]
\[15\ln \,-12lm\,+3{{l}^{2}}\]
?	+	?
\[25\ln \]		\[+5{{l}^{2}}\]

                                        (d) First expression \[=3a(a+b+c)\,-2b(a-b+c)\] \[=(3a)\times (a)+(3a)\times (b)+(3a)\]\[\times (c)-(2b)\times (a)+(2b)\times (b)\]\[-(2b)\times (c)\] \[=3{{a}^{2}}+3ab+3ac-2ab+2{{b}^{2}}-2bc\] \[=3{{a}^{2}}+2{{b}^{2}}+3ab-2ab-2bc+3ac\] \[=3{{a}^{2}}+2{{b}^{2}}+ab-2bc+3ac\] Second expression \[=4c(-a+b+c)\] \[=4c\times (-a)\,+4c\times b+4c\times c\] \[=-4ac+4bc+4{{c}^{2}}\] Subtraction \[\to \]

\[-4ac+4bc+4{{c}^{2}}\]
\[3{{a}^{2}}+2{{b}^{2}}+ab+3ac-2bc\]
?	?	?	?	+
\[-3{{a}^{2}}-2{{b}^{2}}-ab-7ac+6bc+4{{c}^{2}}\]