Question

Преобразуйте выражение в многочлен стандартного видаа)(m+n)^2+(m-n)^2b)2(a-1)^2+3(a-2)^2c)5(x-y)^2+(x-2y)^2d)4(m-2n)^2-3(3m+n)^2e)3(2a-b)-5(a-2b)^2f)4(3x+4y)^2-7(2x-3y)^2g)2(p-3q)^2-4(2p-q)^2-(2q-3p)(p+q)h)5(n-5m)^2-6(2n-3m)^2-(3m-n)(7m-n)i)(2p-q)^2-2(2p-q)(p-q)+(p-q)^2

Answer 1

Перемножит и тогда выйдет кажется всё в квадрате

Answer 2

a) (m + n)^2 + (m - n)^2

To simplify this expression, we can expand the squares and combine like terms.

Expanding the first square: (m + n)^2 = m^2 + 2mn + n^2

Expanding the second square: (m - n)^2 = m^2 - 2mn + n^2

Now, let's combine the terms: (m + n)^2 + (m - n)^2 = (m^2 + 2mn + n^2) + (m^2 - 2mn + n^2)

Combine like terms: = 2m^2 + 2n^2

So, the simplified expression is 2m^2 + 2n^2.

b) 2(a - 1)^2 + 3(a - 2)^2

To simplify this expression, we will expand the squares and combine like terms.

Expanding the first square: (a - 1)^2 = a^2 - 2a + 1

Expanding the second square: (a - 2)^2 = a^2 - 4a + 4

Now, let's combine the terms: 2(a - 1)^2 + 3(a - 2)^2 = 2(a^2 - 2a + 1) + 3(a^2 - 4a + 4)

Distribute the coefficients: = 2a^2 - 4a + 2 + 3a^2 - 12a + 12

Combine like terms: = 5a^2 - 16a + 14

So, the simplified expression is 5a^2 - 16a + 14.

c) 5(x - y)^2 + (x - 2y)^2

To simplify this expression, we will expand the squares and combine like terms.

Expanding the first square: (x - y)^2 = x^2 - 2xy + y^2

Expanding the second square: (x - 2y)^2 = x^2 - 4xy + 4y^2

Now, let's combine the terms: 5(x - y)^2 + (x - 2y)^2 = 5(x^2 - 2xy + y^2) + (x^2 - 4xy + 4y^2)

Distribute the coefficients: = 5x^2 - 10xy + 5y^2 + x^2 - 4xy + 4y^2

Combine like terms: = 6x^2 - 14xy + 9y^2

So, the simplified expression is 6x^2 - 14xy + 9y^2.

d) 4(m - 2n)^2 - 3(3m + n)^2

To simplify this expression, we will expand the squares and combine like terms.

Expanding the first square: (m - 2n)^2 = m^2 - 4mn + 4n^2

Expanding the second square: (3m + n)^2 = 9m^2 + 6mn + n^2

Now, let's combine the terms: 4(m - 2n)^2 - 3(3m + n)^2 = 4(m^2 - 4mn + 4n^2) - 3(9m^2 + 6mn + n^2)

Distribute the coefficients: = 4m^2 - 16mn + 16n^2 - 27m^2 - 18mn - 3n^2

Combine like terms: = -23m^2 - 34mn + 13n^2

So, the simplified expression is -23m^2 - 34mn + 13n^2.

e) 3(2a - b) - 5(a - 2b)^2

To simplify this expression, we will expand the square and distribute the coefficients.

Expanding the square: (a - 2b)^2 = a^2 - 4ab + 4b^2

Now, let's distribute the coefficients: 3(2a - b) - 5(a - 2b)^2 = 3(2a - b) - 5(a^2 - 4ab + 4b^2)

Distribute the first coefficient: = 6a - 3b - 5(a^2 - 4ab + 4b^2)

Distribute the second coefficient: = 6a - 3b - 5a^2 + 20ab - 20b^2

Combine like terms: = -5a^2 + 26ab - 20b^2 + 6a - 3b

So, the simplified expression is -5a^2 + 26ab - 20b^2 + 6a - 3b.

f) 4(3x + 4y)^2 - 7(2x - 3y)^2

To simplify this expression, we will expand the squares and distribute the coefficients.

Expanding the first square: (3x + 4y)^2 = 9x^2 + 24xy + 16y^2

Expanding the second square: (2x - 3y)^2 = 4x^2 - 12xy + 9y^2

Now, let's distribute the coefficients: 4(3x + 4y)^2 - 7(2x - 3y)^2 = 4(9x^2 + 24xy + 16y^2) - 7(4x^2 - 12xy + 9y^2)

Distribute the first coefficient: = 36x^2 + 96xy + 64y^2 - 28x^2 + 84xy - 63y^2

Combine like terms: = 8x^2 + 180xy + 1y^2

So, the simplified expression is 8x^2 + 180xy + 1y^2.

g) 2(p - 3q)^2 - 4(2p - q)^2 - (2q - 3p)(p + q)

To simplify this expression, we will expand the squares and distribute the coefficients.

Expanding the first square: (p - 3q)^2 = p^2 - 6pq + 9q^2

Expanding the second square: (2p - q)^2 = 4p^2 - 4pq + q^2

Now, let's distribute the coefficients: 2(p - 3q)^2 - 4(2p - q)^2 - (2q - 3p)(p + q) = 2(p^2 - 6pq + 9q^2) - 4(4p^2 - 4pq + q^2) - (2q - 3p)(p + q)

Distribute the first coefficient: = 2p^2 - 12pq + 18q^2 - 16p^2 + 16pq - 4q^2 - (2q - 3p)(p + q)

Simplify the expression in the parentheses: = 2p^2 - 12pq + 18q^2 - 16p^2 + 16pq - 4q^2 - (2qp + 2q^2 - 3p^2 - 3pq)

Combine like terms: = -14p^2 - 2q^2 + 12pq - 2qp - 2q^2 + 3p^2 + 3pq

Combine like terms again: = -11p^2 + 13pq - 4q^2

So, the simplified expression is -11p^2 + 13pq - 4q^2.

h) 5(n - 5m)^2 - 6(2n - 3m)^2 - (3m - n)(7m - n)

To simplify this expression, we will expand the squares and distribute the coefficients.

Expanding the first square: (n - 5m)^2 = n^2 - 10nm + 25m^2

Expanding the second square: (2n - 3m)^2 = 4n^2 - 12nm + 9m^2

Now, let's distribute the coefficients: 5(n - 5m)^2 - 6(2n - 3m)^2 - (3m - n)(7m - n) = 5(n^2 - 10nm + 25m^2) - 6(4n^2 - 12nm + 9m^2) - (3m - n)(7m - n)

Distribute the first coefficient: = 5n^2 - 50nm + 125m^2 - 24n^2 + 72nm - 54m^2 - (21m^2 - 7mn - 3mn + n^2)

Combine like terms: = -19n^2 - 25nm + 92m^2 - 21m^2 + 10mn - n^2

Combine like terms again: = -20n^2 + 10mn + 71m^2

So, the simplified expression is -20n^2 + 10mn + 71m^2.

i) (2p - q