Question

№12Преобразуйте в многочлена)(u-v)^2=___б)(10n-3)^2=__в)(c^2-1)^2=___г)((4a^3-b)^2=__д)(3m-1\2)^2=___ж)(6-c)^2=___з)(0,2x-y)^2=__и)(a-3ac)^2=__

Answer 1

А) u²-2uv+v²
б) 100n²-60n+9
в) c^4-2c²+1
г) 16a^6-8a^3b+b²
д) 9m²-3m+1/4
ж) 36-12с+с²
з)  0,04x²+0,4xy+y²
и) a²-6a²c+9a²c²

Answer 2

a) (u-v)^2

To expand the expression (u-v)^2, we can use the formula for squaring a binomial:

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

Applying this formula to our expression, we have:

(u-v)^2 = u^2 - 2uv + v^2

So, the expanded form of (u-v)^2 is u^2 - 2uv + v^2.

б) (10n-3)^2

To expand the expression (10n-3)^2, we can again use the formula for squaring a binomial:

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

Applying this formula to our expression, we have:

(10n-3)^2 = (10n)^2 - 2(10n)(3) + 3^2

Simplifying, we get:

(10n-3)^2 = 100n^2 - 60n + 9

So, the expanded form of (10n-3)^2 is 100n^2 - 60n + 9.

в) (c^2-1)^2

To expand the expression (c^2-1)^2, we can once again use the formula for squaring a binomial:

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

Applying this formula to our expression, we have:

(c^2-1)^2 = (c^2)^2 - 2(c^2)(1) + 1^2

Simplifying, we get:

(c^2-1)^2 = c^4 - 2c^2 + 1

So, the expanded form of (c^2-1)^2 is c^4 - 2c^2 + 1.

г) ((4a^3-b)^2

To expand the expression ((4a^3-b)^2, we once again use the formula for squaring a binomial:

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

Applying this formula to our expression, we have:

((4a^3-b)^2 = (4a^3)^2 - 2(4a^3)(b) + b^2

Simplifying, we get:

((4a^3-b)^2 = 16a^6 - 8a^3b + b^2

So, the expanded form of ((4a^3-b)^2 is 16a^6 - 8a^3b