Алгебра.Дидактические материалы 7 класс.Мерзляк,Полонский,Рабинович,Якир.
Разложите на множители:
1) ab-ac+yb-yc;
2) 3x+3y-bx-by;
3) 4n-nc-4+c;
4) x^7+x^3-4x^4-4;
5) 6mn-3m+2n-1;
6) 4a^4-5a^3y-8a+10y;
7) a^2b^2-a+ab^2-1;
8) xa-xb^2-ya+zb^2-za+yb^2
Разложите на множители:
1) ab-ac+yb-yc;
2) 3x+3y-bx-by;
3) 4n-nc-4+c;
4) x^7+x^3-4x^4-4;
5) 6mn-3m+2n-1;
6) 4a^4-5a^3y-8a+10y;
7) a^2b^2-a+ab^2-1;
8) xa-xb^2-ya+zb^2-za+yb^2
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1) (ab - ac) + (yb - yc) = a(b - c) + y(b -c) = ( b - c)(a +y)2) ( 3x + 3y) - bx - by = 3(x + y) - b(x + y) = (x+y)(3 - b)
3) (4n - 4) + ( c - nc) = 4( n - 1) + c( 1 - n) = (4 - c)(n - 1)
4) ( x⁷ + x³) - 4x⁴ - 4 = x³(x⁴ + 1) - 4( x⁴ + 1) = (x⁴+1)( x³ - 4)
5) (6mn - 3m) + ( 2n - 1) = 3m( 2n - 1) + ( 2n - 1)=(2n - 1)(3m + 1)
6) (4a⁴ - 8a) +(10y - 5ya³) = 4a(a³ - 2) + 5y(2 - a³) = (4a - 5y)(a³ - 2)
7) a²b² - a + ab² - 1 = (a²b² + ab²) - (a + 1) = ab²(a + 1) - (a+1)=(a+1)(ab² - 1)
8) (xa - xb²) + (zb² - za) - ya + yb² = x(a-b²)+z(b² -a) - y(a -b²)=(x - z - y)(a - b²)