Упр.120 Вариант 2 Дидактические материалы ГДЗ Мерзляк Полонский 7 класс (Алгебра)

1) (x-6)(x+6);
2) (3+x)(x-3);
3) (3b-5)(3b+5);
4) (5x+8y)(8y-5x);
5) (m^5-n^3 )(m^5+n^3 );
6) (5a^2 b-1/4 ab^2 )(5a^2 b+1/4 ab^2 );
7) (0,5x^3+0,2y^4 )(0,5x^3-0,2y^4 );
8) (a^5-b^5 )(a^5+b^5 )(a^10+b^10 );
9) (-x^7-y^3 )(y^3-x^7 );
10) (2/3 y^6+1,2x^11 )(1,2x^11-2/3 y^6 ).

1. $$ (x-6)(x+6)=x^2-6^2=x^2-36 $$
2. $$ (3+x)(x-3)=(x+3)(x-3)=x^2-3^2=x^2-9 $$
3. $$ (3b-5)(3b+5)=(3b)^2-5^2=9b^2-25 $$
4. $$ (5x+8y)(8y-5x)=(8y+5x)(8y-5x)=(8y)^2-(5x)^2=64y^2-25x^2 $$
5. $$ (m^5-n^3)(m^5+n^3)=(m^5)^2-(n^3)^2=m^{10}-n^6 $$
6. $$ \left(5a^2b-\frac14ab^2\right)\left(5a^2b+\frac14ab^2\right)=\left(5a^2b\right)^2-\left(\frac14ab^2\right)^2 $$
   $$ =25a^4b^2-\frac1{16}a^2b^4 $$
7. $$ (0{,}5x^3+0{,}2y^4)(0{,}5x^3-0{,}2y^4)=(0{,}5x^3)^2-(0{,}2y^4)^2 $$
   $$ =0{,}25x^6-0{,}04y^8 $$
8. $$ (a^5-b^5)(a^5+b^5)(a^{10}+b^{10})=\bigl((a^5)^2-(b^5)^2\bigr)(a^{10}+b^{10}) $$
   $$ =(a^{10}-b^{10})(a^{10}+b^{10})=(a^{10})^2-(b^{10})^2=a^{20}-b^{20} $$
9. $$ (-x^7-y^3)(y^3-x^7)=-(y^3+x^7)(y^3-x^7) $$
   $$ =-\bigl((y^3)^2-(x^7)^2\bigr)=-(y^6-x^{14})=x^{14}-y^6 $$
10. $$ \left(\frac23y^6+1{,}2x^{11}\right)\left(1{,}2x^{11}-\frac23y^6\right)=\left(1{,}2x^{11}+\frac23y^6\right)\left(1{,}2x^{11}-\frac23y^6\right) $$
    $$ =(1{,}2x^{11})^2-\left(\frac23y^6\right)^2=1{,}44x^{22}-\frac49y^{12} $$

Ответ

1) $$x^2-36$$; 2) $$x^2-9$$; 3) $$9b^2-25$$; 4) $$64y^2-25x^2$$; 5) $$m^{10}-n^6$$; 6) $$25a^4b^2-\frac1{16}a^2b^4$$; 7) $$0{,}25x^6-0{,}04y^8$$; 8) $$a^{20}-b^{20}$$; 9) $$x^{14}-y^6$$; 10) $$1{,}44x^{22}-\frac49y^{12}$$.