Question 15 Marks
सर्वसमिका $a^2-b^2=(a+b)(a-b)$ का प्रयोग करते हुए, निम्न के गुणनखंड कीजिए-
(i) $x^2-9$
(ii) $4 x^2-25 y^2$
(iii) $4 x^2-49 y^2$
(iv) $3 a^2 b^3-27 a^4 b$
(v) $28 a y^2-175 a x^2$
(vi) $9 x^2-1$
(vii) $25 a x^2-25 a$
(viii) $\frac{x^2}{9}-\frac{y^2}{25}$
(ix) $\frac{2 p^2}{25}-32 q^2$
(x) $49 x^2-36 y^2$
(xi) $y^3-\frac{y}{9}$
(xii) $\frac{x^2}{25}-625$
(xiii) $\frac{x^2}{8}-\frac{y^2}{18}$
(xiv) $\frac{4 x^2}{9}-\frac{9 y^2}{16}$
(xv) $\frac{x^3 y}{9}-\frac{x y^3}{16}$
(xvi) $1331 x^3 y-11 y^3 x$
(xvii) $\frac{1}{36} a^2 b^2-\frac{16}{49} b^2 c^2 \quad$ (xviii) $\quad a^4-(a-b)^4$
(xix) $x^4-1$
(xx) $y^4-625$
(xxi) $p^5-16 p$
(xxii) $16 x^4-81$ \begin{aligned}
& \text { (xxiii) } x^4-y^4 \\
& \text { (xxiv) } y^4-81 \\
& \text { (xxv) } 16 x^4-625 y^4 \quad \text { (xxvi) }(a-b)^2-(b-c)^2 \\
& \text { (xxvii) } \quad(x+y)^4-(x-y)^4 \quad \text { (xxviii) } \quad x^4-y^4+x^2-y^2 \\
& \text { (xxix) } 8 a^3-2 a \\
& ( xxx ) \quad x^2-\frac{y^2}{100} \\
& \text { (xxxi) } 9 x^2-(3 y+z)^2 \\
&
\end{aligned}
Answer(i) $(x-3)(x+3)$ (ii) $(2 x-5 y)(2 x+5 y)$ (iii) $(2 x-7 y)(2 x+7 y)$ (iv) $3 a^2 b(b-3 a)(b+3 a)$ (v) $7 a(2 y-5 x)(2 y+5 x)$ (vi) $(3 x-1)(3 x+1)$ (vii) $25 a(x-1)(x+1) \quad$ (viii) $\left(\frac{x}{3}-\frac{y}{5}\right)\left(\frac{x}{3}+\frac{y}{5}\right)$ (ix) $2\left(\frac{p}{5}-4 q\right)\left(\frac{p}{5}+4 q\right)$ (x) $(7 x-6 y)(7 x+6 y)$(xi) $y\left(y-\frac{1}{3}\right)\left(y+\frac{1}{3}\right) \quad$
(xii) $\left(\frac{x}{5}-25\right)\left(\frac{x}{5}+25\right)$
(xiii) $\frac{1}{2}\left(\frac{x}{2}-\frac{y}{3}\right)\left(\frac{x}{2}+\frac{y}{3}\right)$
(xiv) $\left(\frac{2}{3} x-\frac{3}{4} y\right)\left(\frac{2}{3} x+\frac{3}{4} y\right)$
(xv) $x y\left(\frac{x}{3}-\frac{y}{4}\right)\left(\frac{x}{3}+\frac{y}{4}\right)$
(xvi) $11 x y(11 x-y)(11 x+y) \quad$
(xvii) $\quad b^2\left(\frac{1}{6} a-\frac{4}{7} c\right)\left(\frac{1}{6} a+\frac{4}{7} c\right)$
(xviii) b(2a-b) $\left(2 a^2-2 a b+b^2\right) \quad$
(xix) $\quad(x-1)(x+1)\left(x^2+1\right)$
(xx) $(y-5)(y+5)\left(y^2+25\right)$
(xxi) $p(p-2)(p+2)\left(p^2+4\right)$
(xxii) $\quad(2 x-3)(2 x+3)\left(4 x^2+9\right)$
(xxiii) $quad(x-y)(x+y)\left(x^2+y^2\right)$
(xxiv) $\quad(y-3)(y+3)\left(y^2+9\right) \quad$
(xxv) $\quad(2 x-5 y)(2 x+5 y)\left(4 x^2+25 y^2\right)$
(xxvi) $(a-2 b+c)(a-c) \quad$
(xxvii) $8 x y\left(x^2+y^2\right)$
(xxviii) $(x-y)(x+y)\left(x^2+y^2+1\right)$
(xxix) $quad 2 a(2 a-1)(2 a+1)$
(xxx) $(x-\frac{y}{10}\right)\left(x+\frac{y}{10}\right) \quad$
(xxxi) $\quad(3 x-3 y-z)(3 x+3 y+z)$
View full question & answer→Question 25 Marks
निम्न के गुणनखंड कीजिए -
(i) $x^2+15 x+26$
(ii) $x^2+9 x+20$
(iii) $x^2+18 x+65$
(iv) $p^2+14 p+13$
(v) $y^2+4 y-21$
(vi) $y^2-2 y-15$
(vii) $18+11 x+x^2$
(viii) $x^2-10 x+21$
(ix) $x^2-17 x+60$
(x) $x^2+4 x-77$
(xi) $y^2+7 y+12$
(xii) $p^2-13 p-30$
(xiii) $a^2-16 a-80$
Answer(i) $(x+13)(x+2)$ (ii) $(x+5)(x+4)$ (iii) $(x+5)(x+13)$ (iv) $(p+1)(p+13)$ (v) $(y+7)(y-3)$ (vi) $(y-5)(y+3)$ (vii) $(9+x)(2+x)$ (viii) $(x-7)(x-3)$ (ix) $(x-12)(x-5)$ (x) $(x+11)(x-7) \quad$ (xi) $(y+4)(y+3) \quad$ (xii) $(p-15)(p+2)$ (xiii) $(a-20)(a+4)$
View full question & answer→Question 35 Marks
सर्वसमिका $a^2-2 a b+b^2=(a-b)^2$ का प्रयोग करते हुए निम्न के गुणनखंड कीजिए -
(i) $x^2-8 x+16$
(ii) $x^2-10 x+25$
(iii) $y^2-14 y+49$
(iv) $p^2-2 p+1$
(v) $4 a^2-4 a b+b^2$
(vi) $p^2 y^2-2 p y+1$
(vii) $a^2 y^2-2 a b y+b^2$
(viii) $9 x^2-12 x+4$
(ix) $4 y^2-12 y+9$
(x) $\frac{x^2}{4}-2 x+4$ (xi) $a^2 y^3-2 a b y^2+b^2 y$
(xii) $9 y^2-4 x y+\frac{4 x^2}{9}$
Answer(i) $(x-4)(x-4)$ (ii) $(x-5)(x-5)$ (iii) $(x-7)(y-7)$ (iv) $(p-1)(p-1)$ (v) $(2 a-b)(2 a-b)(v i)(p y-1)(p y-1)$ (vii) $(a y-b)(a y-b) \quad$ (viii) $\quad(3 x-2)(3 x-2) \quad$ (ix) $(2 y-3)(2 y-3)$ (x) $\left(\frac{x}{2}-2\right)\left(\frac{x}{2}-2\right) \quad$ (xi) $y(a y-b)(a y-b) \quad$ (xii) $\left(3 y-\frac{2 x}{3}\right)^2$
View full question & answer→Question 45 Marks
सर्वसमिका $a^2+2 a b+b^2=(a+b)^2$ का प्रयोग करते हुए, निम्न के गुणनखंड कीजिए -
(i) $x^2+6 x+9$
(ii) $x^2+12 x+36$
(iii) $x^2+14 x+49$
(iv) $x^2+2 x+1$
(v) $4 x^2+4 x+1$
(vi) $a^2 x^2+2 a x+1$
(vii) $a^2 x^2+2 a b x+b^2$
(viii) $a^2 x^2+2 a b x y+b^2 y^2$
(ix) $4 x^2+12 x+9$
(x) $16 x^2+40 x+25$
(xi) $9 x^2+24 x+16$
(xii) $9 x^2+30 x+25$
(xiii) $2 x^3+24 x^2+72 x$
(xiv) $a^2 x^3+2 a b x^2+b^2 x$
(xv) $4 x^4+12 x^3+9 x^2$
(xvi) $\frac{x^2}{4}+2 x+4$
(xvii) $9 x^2+2 x y+\frac{y^2}{9}$
Answer(i) $(x+3)(x+3)$ (ii) $(x+6)(x+6)$ (iii) $(x+7)(x+7)$ (iv) $(x+1)(x+1)$ (v) $(2 x+1)(2 x+1)$ (vi) $(a x+1)(a x+1)$ (vii) $(a x+b)(a x+b) \quad$ (viii) $(a x+b y)(a x+b y)$ $\begin{array}{ll}\text { (ix) }(2 x+3)(2 x+3) & \text { (x) }(4 x+5)(4 x+5)\end{array}$ (xi) $(3 x+4)(3 x+4) \quad$ (xii) $(3 x+5)(3 x+5)$ (xiii) $2 x(x+6)(x+6) \quad$ (xiv) $x(a x+b)(a x+b)$ (xv) $x^2(2 x+3)(2 x+3)( xvi )\left(\frac{x}{2}+2\right)\left(\frac{x}{2}+2\right) \quad$ (xvii) $\left(3 x+\frac{y}{3}\right)\left(3 x+\frac{y}{3}\right)$
View full question & answer→Question 55 Marks
निम्न व्यंजकों के गुणनखंड कीजिए -
(i) $6 a b+12 b c$
(ii) $-x y-a y$
(iii) $a x^3-b x^2+c x$
(iv) $l^2 m^2 n-l m^2 n^2-l^2 m n^2$
(v) $3 p q r-6 p^2 q^2 r^2-15 r^2$
(vi) $x^3 y^2+x^2 y^3-x y^4+x y$
(vii) $4 x y^2-10 x^2 y+16 x^2 y^2+2 x y$
(viii) $2 a^3-3 a^2 b+5 a b^2-a b$
(ix) $63 p^2 q^2 r^2 s-9 p q^2 r^2 s^2+15 p^2 q r^2 s^2-60 p^2 q^2 r s^2$
(x) $24 x^2 y z^3-6 x y^3 z^2+15 x^2 y^2 z-5 x y z$ (xi) $a^3+a^2+a+1$
(xii) $l x+m y+m x+l y$
(xiii) $a^3 x-x^4+a^2 x^2-a x^3$
(xiv) $2 x^2-2 y+4 x y-x$
(xv) $y^2+8 z x-2 x y-4 y z$
(xvi) $a x^2 y-b x y z-a x^2 z+b x y^2$
(xvii) $a^2 b+a^2 c+a b+a c+b^2 c+c^2 b$
(xviii) $2 a x^2+4 a x y+3 b x^2+2 a y^2+6 b x y+3 b y^2$
Answer(i) $6 b(a+2 c)$
(ii) $-y(x+a)$
(iii) $x\left(a x^2-b x+c\right)$
(iv) $\operatorname{lmn}(l m-m n-l n)$ (v) $3 r\left(p q-2 p^2 q^2 r-5 r\right)$
(vi) $x y\left(x^2 y+x y^2-y^3+1\right) \quad$ (vii) $2 x y(2 y-5 x+8 x y+1)$
(viii) $a\left(2 a^2-3 a b+5 b^2-b\right)$
(ix) $3 p q r s(21 p q r-3 q r s+5 p r s-20 p q s)$
(x) $x y z\left(24 x z^2-6 y^2 z+15 x y-5\right)$
(xi) $(a+1)\left(a^2+1\right)$
(xii) $(x+y)(l+m) \quad$ (xiii) $x(a+x)(a-x)(a+x)$
(xiv) $(x+2 y)(2 x-1)$
(xv) $(y-4 z)(y-2 x) \quad$ (xvi) $x(a x+b y)(y-z)$
(xvii) $\left(a^2+a+b c\right)(b+c) \quad$
(xviii) $(2 a+3 b)(x+y)(x+y)$
View full question & answer→Question 65 Marks
निम्न पदों में महत्तम (सबसे बड़ा) सार्व गुणनखंड ज्ञात कीजिए -
(i) $-18 a^2, 108 a$
(ii) $3 x^2 y, 18 x y^2,-6 x y$
(iii) $2 x y,-y^2, 2 x^2 y$
(iv) $l^2 m^2 n, l m^2 n^2, l^2 m n^2$
(v) $21 p q r,-7 p^2 q^2 r^2, 49 p^2 q r$
(vi) qrxy, pryz, rxyz
(vii) $3 x^3 y^2 z,-6 x y^3 z^2, 12 x^2 y z^3$
(viii) $63 p^2 a^2 r^2 s,-9 p q^2 r^2 s^2, 15 p^2 q r^2 s^2,-60 p^2 a^2 r s^2$
(ix) $13 x^2 y, 169 x y$
(x) $11 x^2, 12 y^2$
Answer(i) 18a (ii) 3xy (iii) y(iv) lmn (v) 7pqr (vi) ry(vii) 3xyz (viii) 3prs (ix) 13xy(x) 1
View full question & answer→Question 75 Marks
उपयुक्त सर्वसमिकाओं का प्रयोग करते हुए, निम्न के मान निकालिए -
(i) $(52)^2$
(ii) $(49)^2$
(iii) $(103)^2$
(iv) $(98)^2$
(v) $(1005)^2$
(vi) $(995)^2$
(vii) $47 \times 53$
(viii) $52 \times 53$
(ix) $105 \times 95$
(x) $104 \times 97$
(xi) $101 \times 103$
(xii) $98 \times 103$ \begin{aligned}
\text { (xiii) } & (9.9)^2 & \text { (xiv) } & 9.8 \times 10.2 \\
(\text { xv) } & 10.1 \times 10.2 & (\text { xvi) } & (35.4)^2-(14.6)^2 \\
(\text { xvii) } & (69.3)^2-(30.7)^2 & (\text { xviii) } & (9.7)^2-(0.3)^2 \\
(\text { xix) } & (132)^2-(68)^2 & (x x) & (339)^2-(161)^2 \\
( xxi ) & (729)^2-(271)^2 & &
\end{aligned}
Answer(i) 2704 (ii) 2401 (iii) 10609(iv) 9604 (v) 1010025 (vi) 990025(vii) 2491 (viii) 2756 (ix) 9975(x) 10088 (xi) 10403 (xii) 10094(xiii) 98.01 (xiv) 99.96 (xv) 103.02(xvi) 1040 (xvii) 3860 (xviii) 94(xix) 12800 (xx) 89000 (xxi) 458000
View full question & answer→Question 85 Marks
उपयुक्त सर्वसमिकाओं का प्रयोग करते हुए, निम्न को प्रसारित कीजिए -
<br/>(i) $(x y+y z)^2$
<br/>(ii) $\left(x^2 y-x y^2\right)^2$
<br/>(iii) $\left(\frac{4}{5} a+\frac{5}{1} b\right)^2$
(iv) $\left(\frac{2}{3} x-\frac{3}{2} y\right)^2$
(v) $\left(\frac{4}{5} p+\frac{5}{3} q\right)^2$
(vi) $(x+3)(x+7)$
(vii) $\quad(2 x+9)(2 x-7)$
(viii) $\left(\frac{4 x}{5}+\frac{y}{4}\right)\left(\frac{4 x}{5}+\frac{3 y}{4}\right)$
(ix) $\left(\frac{2 x}{3}-\frac{2 a}{3}\right)\left(\frac{2 x}{3}+\frac{2 a}{3}\right)$
(x) $(2 x-5 y)(2 x-5 y)$
(xi) $\left(\frac{2 a}{3}+\frac{b}{3}\right)\left(\frac{2 a}{3}-\frac{b}{3}\right)$
(xii) $\left(x^2+y^2\right)\left(x^2-y^2\right)$
(xiii) $\left(a^2+b^2\right)^2$
(xiv) $(7 x+5)^2$ (xv) $(0.9 p-0.5 q)^2$
(xvi) $\left(36 a ^2-4 ab ^2\right)^2$
Answer(i) $x^2 y^2+2 x y^2 z+y^2 z^2$
(ii) $x^4 y^2-2 x^3 y^3+x^2 y^4$
(iii) $\frac{16}{25} a^2+2 a b+\frac{25}{16} b^2$
(iv) $\frac{4}{9} x^2-2 x y+\frac{9}{4} y^2$
(v) $\frac{16}{25} p^2+\frac{8}{3} p q+\frac{25}{9} q^2$
(vi) $x^2+10 x+21$
(vii) $4 x^2+4 x-63$
(viii) $\frac{16}{25} x^2+\frac{4 x y}{5}+\frac{3 y^2}{16}$
(ix) $\frac{4}{9} x^2-\frac{4}{9} a^2$
(x) $4 x^2-20 x y+25 y^2$
(xi) $\frac{4}{9} a^2-\frac{b^2}{9}$
(xii) $x^4-y^4$
(xiii) $a^4+2 a^2 b^2+b^4$
(xiv) $49 x^2+70 x+25$
(xv) $0.81 p^2-0.9 p q+0.25 q^2 \quad$ (xvi) $1296 a^4+2401 b^4-3528 a^2 b^2$
View full question & answer→Question 95 Marks
सरल कीजिए -
(i) $(3 x+2 y)^2+(3 x-2 y)^2$
(ii) $(3 x+2 y)^2-(3 x-2 y)^2$
(iii) $\left(\frac{7}{9} a+\frac{9}{7} b\right)^2-a b$
(iv) $\left(\frac{3}{4} x-\frac{4}{3} y\right)^2+2 x y$
(v) $(1.5 p+1.2 q)^2-(1.5 p-1.2 q)^2$
(vi) $(2.5 m+1.5 q)^2+(2.5 m-1.5 q)^2$
(vii) $\left(x^2-4\right) \times\left(x^2+4\right)+16$
(viii) $(a b-c)^2+2 a b c$
(ix) $(a-b)\left(a^2+b^2+a b\right)-(a+b)\left(a^2+b^2-a b\right)$
(x) $\left(b^2-49\right)(b+7)+343$
(xi) $(4.5 a+1.5 b)^2+(4.5 b+1.5 a)^2$
(xii) $(p q-q r)^2+4 p q^2 r$
(xiii) $\quad\left(s^2 t+t q^2\right)^2-(2 s t q)^2$
Answer(i) $18 x^2+8 y^2$
(ii) $24 x y$
(iii) $\frac{49}{81} a^2 a b+\frac{81}{49} b^2$
(iv) $\frac{9}{16} x^2+\frac{16}{9} y^2$
(v) $7.2 p q$
(vi) $12.5 m^2+4.5 q^2$
(vii) $x^4$
(viii) $a^2 b^2+c^2$
(ix) $-2 b^3$
(x) $b^3-49 b+7 b^2$
(xi) $40.5 a^2+27 a b+4.5 b^2$
(xii) $p^2 q^2+2 p q^2 r+q^2 r^2$
(xiii) $s^4 t^2-2 s^2 t^2 q^2+t^2 q^4$
View full question & answer→Question 105 Marks
निम्न को गुणा कीजिए -
(i) $-7 p q^2 r^3,-13 p^3 q^2 r$
(ii) $3 x^2 y^2 z^2, 17 x y z$
(iii) $15 x y^2, 17 y z^2$
(iv) $-5 a^2 b c, 11 a b, 13 a b c^2$
(v) $-3 x^2 y,(5 y-x y)$
(vi) $a b c,(b c+c a)$
(vii) $7 p q r,(p-q+r)$
(viii) $x^2 y^2 z^2,(x y-y z+z x)$
(ix) $(p+6),(q-7)$
(x) $6 m n, 0 m n$
(xi) $a, a^5, a^6$
(xii) $-7 s t,-1,-13 s t^2$ (xiii) $b^3, 3 b^2, 7 a b^5$
$\text { (xiv) }-\frac{100}{9} r s ; \frac{3}{4} r^3 s^2$
(xv) $\left(a^2-b^2\right),\left(a^2+b^2\right)$
(xvi) $(a b+c),(a b+c)$
(xvii) $(p q-2 r),(p q-2 r)$
(xviii) $\left(\frac{3}{4} x-\frac{4}{3} y\right),\left(\frac{2}{3} x+\frac{3}{2} y\right)$
( $xx ) \quad\left(x^2-5 x+6\right),(2 x+7)$
(xxi) $\left(3 x^2+4 x-8\right),\left(2 x^2-4 x+3\right)$
(xxii) $\quad(2 x-2 y-3),(x+y+5)$
Answer(i) $91 p^4 q^4 r^4$
(ii) $51 x^3 y^3 z^3$
(iii) $255 x y^3 z^2$
(iv) $-715 a^4 b^3 c^3$
(v) $-15 x^2 y^2+3 x^3 y^2$
(vi) $a b^2 c^2+a^2 b c^2$
(vii) $7 p^2 q r-7 p q^2 r+7 p q r^2$
(viii) $x^3 y^3 z^2-x^2 y^3 z^3+x^3 y^2 z^3$
(ix) $p q-7 p+6 q-42$
(x) 0
(xi) $a^{12}$
(xii) $-91 S ^2 t^3$
(xiii) $21 a b^{10}$
(xiv) $-\frac{25}{3} r^4 s^3$
(xv) $a^4-b^4$
(xvi) $a^2 b^2+2 a b c+c^2$
(xvii) $p^2 q^2-4 p q r+4 r^2$
(xviii) $\frac{1}{2} x^2+\frac{17}{72} x y-2 y^2$
(xix) $3 p^4-\frac{19}{6} p^2 q^2-2 q^4$
(xx) $2 x^3-3 x^2-23 x+42$
(xxi) $6 x^4-4 x^3-23 x^2+44 x-24$ (xxii) $2 x^2+7 x-13 y-2 y^2-15$
View full question & answer→Question 115 Marks
घटाइए -
(i) $5 a^2 b^2 c^2$ में से $-7 a^2 b^2 c^2$
(ii) $6 x^2-4 x y+5 y^2$ में से $8 y^2+6 x y-3 x^2$
(iii) $2 a b^2 c^2+4 a^2 b^2 c-5 a^2 b c^2$ में से $-10 a^2 b^2 c+4 a b^2 c^2+2 a^2 b c^2$
(iv) $3 t^4-4 t^3+2 t^2-6 t+6$ में से $-4 t^4+8 t^3-4 t^2-2 t+11$
(v) $2 a b+5 b c-7 a c$ में से $5 a b-2 b c-2 a c+10 a b c$
(vi) $7 p(3 q+7 p)$ में से $8 p(2 p-7 q)$
(vii) $-3 p^2+3 p q+3 p x$ में से $3 p(-p-a-r)$
Answer(i) $-12 a^2 b^2 c^2$
(ii) $-9 x^2+10 x y+3 y^2$
(iii) $2 a b^2 c^2-14 a^2 b^2 c+7 a^2 b c^2$
(iv) $-7 t^4+12 t^3-6 t^2+4 t+5$
(v) $3 a b-7 b c+5 a c+10 a b c$
(vi) $-33 p^2-77 p q$
(vii) $-3 a p-3 p r-3 p q-3 p x$
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जोड़िए -(i) $7 a^2 b c,-3 a b c^2$ और $3 a^2 b c, 2 a b c^2$, (ii) $9 a x,+3 b y-c z$ और $-5 b y+a x+3 c z$, (iii) $x y^2 z^2+3 x^2 y^2 z-4 x^2 y z^2$ और $-9 x^2 y^2 z+3 x y^2 z^2+x^2 y z^2$, (iv) $5 x^2-3 x y+4 y^2-9$ और $7 y^2+5 x y-2 x^2+13$, (v) $2 p^4-3 p^3+p^2-5 p+7$ और $-3 p^4-7 p^3-3 p^2-p-12$, (vi) $3 a(a-b+c)$ और $2 b (a-b+c)$, (vii) $3 a(2 b+5 c)$ और $3 c(2 a+2 b)$
Answer(i) $10 a^2 b c-a b c^2$
(ii) $10 a x-2 b y+2 c z$
(iii) $4 x y^2 z^2-6 x^2 y^2 z-3 x^2 y z^2$
(iv) $3 x^2+2 x y+11 y^2+4$
(v) $-p^4-10 p^3-2 p^2-6 p-5$
(vi) $3 a^2-a b+3 a c+2 b c-2 b^2$
(vii) $6 a b+21 a c+6 b c$
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निम्नांकित प्रश्नों का सत्यापन कीजिए -
(i) $(a b+b c)(a b-b c)+(b c+c a)(b c-c a)+(c a+a b)(c a-a b)=0$
(ii) $(a+b+c)\left(a^2+b^2+c^2-a b-b c-c a\right)=a^3+b^3+c^3-3 a b c$
(iii) $(p-q)\left(p^2+p q+q^2\right)=p^3-q^3$
(iv) $(m+n)\left(m^2-m n+n^2\right)=m^3+n^3$ (v) $(a+b)(a+b)(a+b)=a^3+3 a^2 b+3 a b^2+b^3$
(vi) $\quad(a-b)(a-b)(a-b)=a^3-3 a^2 b+3 a b^2-b^3$
(vii) $\left.\left(a^2-b^2\right)\left(a^2+b^2\right)+\left(b^2-c^2\right)\left(b^2+c^2\right)+\left(c^2-a^2\right)\right)+\left(c^2+a^2\right)=0$
(viii) $(5 x+8)^2-160 x=(5 x-8)^2$
(ix) $(7 p-13 q)^2+364 p q=(7 p+13 q)^2$
(x) $\left(\frac{3 p}{7}+\frac{7}{6 p}\right)^2-\left(\frac{3}{7} p+\frac{7}{6 p}\right)^2=2$
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