Сократите дробь m^3+8*^3/4c^2-2cm+m^2 27x^6-y^3/9x^4+3x^2y+y^2

Question

Алгебра: Сократите дробь m^3+8*^3/4c^2-2cm+m^2 27x^6-y^3/9x^4+3x^2y+y^2

stasison · Accepted Answer

1)
9х²-12х+5 = ((3х)² - 2·3х·2+2²) - 2² + 5 = (3х-2)²+1;

65+16с² +с⁴ = с⁴+16с+65 = ((с²)² + 2·с²·8 + 8²)-8²+65 = (с²-8)² -64+65=
= (с²-8)²+1;

4а² – 40а + 1 = ((2а)² - 2·2а·10+10²)-10²+1 = (2а-10)² - 100+1=(2а-10)²-99.

m² +5mn + n² = (m²+2mn+n²) - 2mn+5mn = (m+n)²+3mn.

х² - 6ху+у² = (x²-2xy+y²)+2xy-6xy = (x-y)² - 4xy.

9а²+7аb+4b² = ((3a)²+2·3a·2b+(2b)²) -12ab+7ab = (3a+2b)²-5ab.

2)
• (5а— 3b) + (6b – 7b+4c) = 5а— 3b + 6b – 7b+4c = 5a - 4b + 4c.

• (6у – 8x+9z) – (11z – 13х + 4у) = 6у – 8x+9z – 11z + 13х - 4у =
= 5x + 2y - 2z.

• 3х(5х – у) – 5у(2у-7х) = 15x² – 3xу – 10y² + 35xy = 15x²+32xy-10y².

• (7a – 9b)(4b + 3a) = 28ab-36b²+21a²-27ab = 21a²+ab-36b².

• (7m –10)(2 – 9m) = 14m-20-63m²+90m = -63m²+104m-20.

• (3c – 4b) = 3c - 4b.

MOGZ ответил