Algebraic Expressions

Rohan’s mother gave him ₹ 3xy² and his father gave him ₹ 5(xy² + 2). Out of this total money he spent ₹ (10 – 3xy²) on his birthday party. How much money is left with him?

Find the value of t if the value of 3x² + 5x – 2t equals to 8, when x = -1.

Identify the constant terms in the following expressions:

(i) -3 +3/2 x

(ii) 3/2 – 5y + y²

(iii) 3x² + 2y – 1

Identify in the given expressions, terms which are not constants. Give their numerical coefficients.

(i) 5x – 3

(ii) 11 – 2y²

(iii) 2x – 1

(iv) 4x²y + 3xy² – 5

From the sum of 2x² + 3xy – 5 and 7 + 2xy – x² subtract 3xy + x² – 2.

Subtract 3x² – x from 5x – x².

Identify the pairs of like and unlike terms:

(i) (-3)/2x, y

(ii) -x, 3x

(iii) (-1)/2y2x, 3/2xy²

(iv) 1000, -2

Add:

(i) 3x²y, -5x²y, -x²y

(ii) a + b – 3, b + 2a – 1

Subtract the sum of -3x³y² + 2x²y³ and -3x²y³ – 5y⁴ from x⁴ + x³y² + x²y³ + y⁴.

What should be subtracted from 2x³ – 3x²y + 2xy² + 3y² to get x³ – 2x²y + 3xy² + 4y²?

Simplify the following expressions and then find the numerical values for x = -2.

(i) 3(2x – 4) + x² + 5

(ii) -2(-3x + 5) – 2(x + 4)

Find the perimeter of the given figure ABCDEF.

If P = 2x² – 5x + 2, Q = 5x² + 6x – 3 and R = 3x² – x – 1. Find the value of 2P – Q + 3R.

To what expression must 99x³ – 33x² – 13x – 41 be added to make the sum zero?

Simplify combining the like terms:

(i) a – (a – b) – b – (b – a)

(ii) x² – 3x + y² – x – 2y²

If A = -(2x + 3), B = -3(x – 2) and C = -2x + 7. Find the value of k if (A + B + C) = kx.

Group the like terms together from the following expressions:

-8x²y, 3x, 4y, (-3)/2x , 2x²y, -y

Classify the following into monomials, binomial and trinomials.

(i) -6

(ii) -5 + x

(iii) x – y

(iv) 6x² + 5x – 3

(v) z² + 2

Draw the tree diagram for the given expressions:

(i) -3xy + 10

(ii) x² + y²

Subtract 3x² – 5y – 2 from 5y – 3x² + xy and find the value of the result if x = 2, y = -1.