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ГДЗ Алгебра 8 клас Істер (2025)
Розділ 1. РАЦІОНАЛЬНІ ВИРАЗИ
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5.23 Виконайте дії:
1) ((25x^2)/(8y^3 ))3 • (–(16y^5)/(125x^3 ))2 = ((5^2 )^3• x^6 • (2^4 )^2 • y^10)/((2^3 )^3•〖 y〗^9 • (5^3 )^2 • x^6 ) = ( 5^6 • 2^8 • y)/(2^(9 )• 5^6 ) = y/2;
2) ( x^2-2xy+ y^2)/(x^2+2xy+ y^2 ) • ((x+ y)/(x- y))3 = ((x- y)^2 (x+ y)^3)/((x+ y)^2 (x- y)^3 ) = (x+ y)/(x- y).
5.24 Виконайте дії:
1) (–(16m^3)/(27n^5 ))2 • ((9n^4)/(8m^2 ))3 = ((2^4 )^2 •〖 m〗^6• (3^2 )^3•〖 n〗^12)/((3^3 )^2 • n^10 • (2^3 )^3 •〖 m〗^6 ) = (2^8 • 3^6• n^2)/(3^6 • 2^9 ) = n^2/2;
2) ((m- n)/(m+ n))3 • (m^2+ 2mn + n^2)/(m^2-2mn + n^2 ) = ((m- n)^3 (m+ n)^2)/((m+ n)^3 (m-n)^2 ) = (m- n)/(m+ n).
1) ((25x^2)/(8y^3 ))3 • (–(16y^5)/(125x^3 ))2 = ((5^2 )^3• x^6 • (2^4 )^2 • y^10)/((2^3 )^3•〖 y〗^9 • (5^3 )^2 • x^6 ) = ( 5^6 • 2^8 • y)/(2^(9 )• 5^6 ) = y/2;
2) ( x^2-2xy+ y^2)/(x^2+2xy+ y^2 ) • ((x+ y)/(x- y))3 = ((x- y)^2 (x+ y)^3)/((x+ y)^2 (x- y)^3 ) = (x+ y)/(x- y).
5.24 Виконайте дії:
1) (–(16m^3)/(27n^5 ))2 • ((9n^4)/(8m^2 ))3 = ((2^4 )^2 •〖 m〗^6• (3^2 )^3•〖 n〗^12)/((3^3 )^2 • n^10 • (2^3 )^3 •〖 m〗^6 ) = (2^8 • 3^6• n^2)/(3^6 • 2^9 ) = n^2/2;
2) ((m- n)/(m+ n))3 • (m^2+ 2mn + n^2)/(m^2-2mn + n^2 ) = ((m- n)^3 (m+ n)^2)/((m+ n)^3 (m-n)^2 ) = (m- n)/(m+ n).