Question

Упростите выражение 1)a) (2а-b)(2а+b)+b2б) (x+7)2-10xв) 9x2-(c+3x)(c-3x)г) 5b2-(a-2b)22)а)(a-c)(a+c)-(a-2c)2б)(x+3)2-(x-3)2в)(a+3c)2+(b+3c)(b-3c)г)(x-4y)2+(x+4y)2д)(x-3)(x+3)-(x+8)(x-8)е)(2a+1)(2a-1)+(a-7)(a+7)​

Answer 1

Ответ:

Пошаговое объяснение:

1)

a) (2а-b)(2а+b)+b^2 =4a^2-b^2+b^2=4a^2

б) (x+7)^2-10x =x^2+14x+49-10x=x^2+4x+49

в) 9x^2-(c+3x)(c-3x) =9x^2-c^2+9x^2=18x^2-c^2

г) 5b^2-(a-2b)^2 =5b^2-a^2+4ab-4b^2=b^2-a^2+4ab

2)

а)(a-c)(a+c)-(a-2c)^2= a^2-c^2-a^2+4ac-4c^2=4ac-5c^2

б)(x+3)^2-(x-3)^2 =x^2+6x+9-x^2+6x-9=12x

в)(a+3c)^2+(b+3c)(b-3c) =a^2+6ac+9c^2+b^2-9c^2=a^2+b^2+6ac

г)(x-4y)^2+(x+4y)^2 =x^2-8xy+16y^2+x^2+8xy+16y^2=2x^2+32y^2

д)(x-3)(x+3)-(x+8)(x-8) =x^2-9-x^2+64=55

е)(2a+1)(2a-1)+(a-7)(a+7)​=4a^2-1+a^2-49=5a^2-50

Answer 2

a) (2a - b)(2a + b) + b^2 = (4a^2 - b^2) + b^2 = 4a^2

b) (x + 7)^2 - 10x = x^2 + 14x + 49 - 10x = x^2 + 4x + 49

c) 9x^2 - (c + 3x)(c - 3x) = 9x^2 - (c^2 - (3x)^2) = 9x^2 - c^2 + 9x^2 = 18x^2 - c^2

d) 5b^2 - (a - 2b)^2 = 5b^2 - (a^2 - 4ab + 4b^2) = 5b^2 - a^2 + 4ab - 4b^2 = -a^2 + 9b^2 + 4ab

a) (a - c)(a + c) - (a - 2c)^2 = a^2 - c^2 - (a^2 - 4ac + 4c^2) = a^2 - c^2 - a^2 + 4ac - 4c^2 = -3c^2 + 4ac

b) (x + 3)^2 - (x - 3)^2 = x^2 + 6x + 9 - (x^2 - 6x + 9) = x^2 + 6x + 9 - x^2 + 6x - 9 = 12x

c) (a + 3c)^2 + (b + 3c)(b - 3c) = a^2 + 6ac + 9c^2 + (b^2 - (3c)^2) = a^2 + 6ac + 9c^2 + b^2 - 9c^2 = a^2 + b^2 + 6ac

d) (x - 4y)^2 + (x + 4y)^2 = x^2 - 8xy + 16y^2 + x^2 + 8xy + 16y^2 = 2x^2 + 32y^2

e) (2a + 1)(2a - 1) + (a - 7)(a + 7) = 4a^2 - 1 + (a^2 - 49) = 5a^2 - 50