Question

anyone answer this question please wrong answer will be reported​

Answer 1

A1)

Terms which are not constants in the following expressions with their numerical coefficients:

1. xy (Numerical coefficient: 1)
2. -y² (Numerical coefficient: -1)
3. -y (Numerical coefficient: -1), 5y² (Numerical coefficient: 5)
4. 4p²q (Numerical coefficient: 4), -3pq² (Numerical coefficient: -3)

A2)

(a) Coefficients of x in the following expressions are:

• 4x - 3y (Coefficient of x: 4)
• 8 - x + y (Coefficient of x: -1)
• y²x - y (Coefficient of x: y²)
• 2z - 5xz (Coefficient of x: 5z)

(b) Coefficient of y in the following expressions are:

• 4x - 3y (Coefficient of y: -3)
• 8 + yz (Coefficient of y: z)
• yz² + 5 (Coefficient of y: z²)
• my + m (Coefficient of y: m)

A3)

The following expressions classified as monomials, binomials and trinomials are:

1. Monomials: xy, 7
2. Binomials: a + b, xy + 5, 4mn + 7
3. Trinomials: ab + a +  b, 5x² - x +2, 4pq - 3q + 5p, 4m - 7n + 10
4. Other (Polynomials): ab + a + b -5

A4)

$12m^{2} - 9m + 5m - 4m^{2} - 7m + 10 = (12m^{2} - 4m^{2}) + (5m - 9m - 7m) +10 \\ \\ (12m^{2} - 4m^{2}) + (5m - 9m - 7m) +10 = 8m^{2} - 11m + 10$

Therefore, answer = 8m² - 11m + 10

A5)

(i) m - n, m + n

Adding: m - n + m + n = 2m

Subtracting: m - n - (m + n) = m - n - m - n = -2n

(ii) mn + 5 - 2, mn + 3

Adding: mn + 5 - 2 + mn + 3 = 2mn + 6

Subtracting: mn + 5 - 2 - (mn + 3) =  mn + 5 - 2 - mn - 3 = 0

A6)

$(30ab + 12b + 14a) - (24ab - 10b - 18a) = (30ab - 24ab) + (12b + 10b) + (14a + 18a) \\ \\ (30ab - 24ab) + (12b + 10b) + (14a + 18a) = 6ab + 22b + 32a$

A7)

$(2y^{2} + 3yz) + (-y^{2}-yz-z^{2})+(yz+2z^{2})=(2y^{2}-y^{2})+(3yz-yz+yz)+(-z^{2}+2z^{2}) \\ \\ (2y^{2}-y^{2})+(3yz-yz+yz)+(-z^{2}+2z^{2})=y^{2}+3yz+z^{2}$

$3y^{2}-z^{2})+(-y^{2}+yz+z^{2})=(3y^{2}-y^{2})+(z^{2}-z^{2})+yz \\ \\ (3y^{2}-y^{2})+(z^{2}-z^{2})+yz=2y^{2}+0+yz=2y^{2}+yz$

$(y^{2}+3yz+z^{2})-(2y^{2}+yz)=(y^{2}-2y^{2})+(3yz-yz)+z^{2} \\ \\ (y^{2}-2y^{2})+(3yz-yz)+z^{2}=-y^{2}+2yz+z^{2}$

Therefore, answer is -y² + 2yz + z²

A8)

The following polynomials classified as monomials, binomials and trinomials are:

1. Monomials: 17
2. Binomials: -z + 5, ab - ac
3. Trinomials: x + y + z, y + z + 100