Question

Упростите выражение 1) (x-2)(x-11)-2x(4-3x) 2) (a+6)(a-3)+(a-4)(a+5) 3) (y-8)(2y-1)-(3y+1)(5y-2) 4) (3m-4n)(3m+5n)-(4.5m-n)(2m+4n) 5) (x^2+2y)(x^3+7y)-6x^3(x2-3y)

Answer 1

1)x^2-11x-2x+22-8x+6x^2=7x^2-21x+22=
7x(x-3)+22
2)a^2-3a+6a-18+(a^2+5a-4a-20)=a^2+3a-
18+a^2+a-20=2a^2+4a-38=2a(a+2)-38
3)2y^2-y-16y+8-(15y^2-6y+5y-2)=
2y^2-17y+8-15y^2-y-2=-13y^2-18y+6=
=-y(13y+18)+6
4)

Answer 2

1) (x-2)(x-11)-2x(4-3x)+2 First, let's multiply (x-2) and (x-11) using the distributive property: (x-2)(x-11) = x^2 - 11x - 2x + 22 = x^2 - 13x + 22 Next, multiply -2x by (4-3x): -2x(4-3x) = -8x + 6x^2 Now, combine all the terms: x^2 - 13x + 22 - 8x + 6x^2 + 2 Simplify by combining like terms: 7x^2 - 21x + 24

2) (a+6)(a-3)+(a-4)(a+5)+3 First, let's multiply (a+6) and (a-3) using the distributive property: (a+6)(a-3) = a^2 - 3a + 6a - 18 = a^2 + 3a - 18 Next, multiply (a-4) by (a+5): (a-4)(a+5) = a^2 + 5a - 4a - 20 = a^2 + a - 20 Now, combine all the terms: a^2 + 3a - 18 + a^2 + a - 20 + 3 Simplify by combining like terms: 2a^2 + 4a - 35

3) (y-8)(2y-1)-(3y+1)(5y-2)+4 First, let's multiply (y-8) and (2y-1) using the distributive property: (y-8)(2y-1) = 2y^2 - y - 16y + 8 = 2y^2 - 17y + 8 Next, multiply (3y+1) by (5y-2): (3y+1)(5y-2) = 15y^2 - 6y + 5y - 2 = 15y^2 - y - 2 Now, combine all the terms: 2y^2 - 17y + 8 - 15y^2 + y + 2 + 4 Simplify by combining like terms: -13y^2 - 15y + 14

4) (3m-4n)(3m+5n)-(4.5m-n)(2m+4n)+5 First, let's multiply (3m-4n) and (3m+5n) using the distributive property: (3m-4n)(3m+5n) = 9m^2 + 15mn - 12mn - 20n^2 = 9m^2 + 3mn - 20n^2 Next, multiply (4.5m-n) by (2m+4n): (4.5m-n)(2m+4n) = 9m^2 + 18mn - 4.5mn - 8n^2 = 9m^2 + 13.5mn - 8n^2 Now, combine all the terms: 9m^2 + 3mn - 20n^2 - 9m^2 - 13.5mn + 8n^2 + 5 Simplify by combining like terms: -10.5mn - 12n^2 + 5

5) (x^2+2y)(x^3+7y)-6x^3(x^2-3y) First, let's multiply (x^2+2y) and (x^3+7y) using the distributive property: (x^2+2y)(x^3+7y) = x^5 + 7x^2y + 2yx^3 + 14y^2 Next, distribute -6x^3 to (x^2-3y): -6x^3(x^2-3y) = -6x^5 + 18x^3y Now, combine all the terms: x^5 + 7x^2y + 2yx^3 + 14y^2 - 6x^5 + 18x^3y Simplify by combining like terms: -5x^5 + 2yx^3 + 7x^2y + 18x^3y + 14y^2