Algebraic Expressions Test - 5

Sum of the former given terms, S₁ = 2x² + 3y²
Sum of the latter given terms, S₂ = -2x² - 4y²
Now, S₂ - S₁ = -2x² - 4y² - 2x² - 3y² = -4x² - 7y²

An algebraic expression that has two terms is called a binomial.
3x + 4y and bx + c are examples of binomials.

So, among the given expressions, 6 + a³ is a binomial.

5b⁹ + 7b⁴ + 4b² - 6b + 0
The degree of a polynomial is the highest degree of its monomials (individual terms) with non-zero coefficients.

The largest degree of b is 9.
So, the degree of the given expression is 9.

Given:
P = 45a³ - 21a² + 12a + 10
Q = -60a² + 35a + 8
R = 9a³ - 64a² - 5

Now, P + Q - R = 45a³ - 21a² + 12a + 10 + (-60a² + 35a + 8) - (9a³ - 64a² - 5)
= 45a³ - 21a² + 12a + 10 - 60a² + 35a + 8 - 9a³ + 64a² + 5

= 45a³ - 9a³ - 21a² - 60a² + 64a² + 12a + 35a + 10 + 8 + 5
= 36a³ - 17a² + 47a + 23

(1) 5x - 7y² - 7y = 2y - 7x² (It is incorrect.)

(2) 7xy - (-8xy) = 15xy (It is correct.)

(3) -3x² - x² = -4x² (It is correct.)

(4) 5x + 7x + (-6x) = 6x (It is correct.)

Given:

(4y - 5 + 2x)(3x + 5y - 7) + {(7x - 5xy + 12) - (8x - 3y + 9)}

On solving the expression, we get

(12xy + 20y² - 28y - 15x - 25y + 35 + 6x² + 10xy - 14x) + (7x - 5xy + 12 - 8x + 3y - 9)

= (6x² + 20y² + 22xy - 29x - 53y + 35) + (-x + 3y - 5xy + 3)

= 6x² + 20y² + 22xy - 29x - 53y + 35 - x + 3y - 5xy + 3

= 6x² + 20y² + 17xy - 30x - 50y + 38

Let x is a number which is subtracted from 6m + 2n² + 3n

Then,
6m + 2n² + 3n - x = 4m + 1 - 3n²
x = 6m + 2n² + 3n - 4m - 1 + 3n²
x = 2m + 5n² + 3n - 1

An expression with two terms is called a binomial.

An expression with three unlike terms is called a trinomial, where unlike terms are the terms having different algebraic factors.

So, 4x + 4y + 7 is a trinomial expression.