Algebraic Expre...

Multiply 4x⁴ + x³ + y² by 2x² + y.

Which of the following is not a standard identity for algebraic expressions? (Where a and b are two variables)

Simplify .

Square of (4y - 2xy) is

If , then find the value of .

If 4x + 3y = 30 and = 3, then find the value of 2x + 4y².

The product of (2xy + 3x² + 6xy²) and (x² + y) is

Find the missing term in the following equation:

= ?

What should be subtracted from 6x² + 4y + 8 to get 3x² + 10y + 4 as the result?

Simplify:

.

What must be added to 16y² - 4y + 8 to get 6y² - 2y - 4 as the result?

If , then find the value of .

Multiply by .

Simplify the following expression:

Find the value of 'a' if and xy = 2.

Thomas is making a cuboidal box for his craft class at school. The length and breadth of the box are 7ab and 4a²b²bc². If the volume of the box is 84a³b⁴c⁵, then find the height of the box.

Sahil works as a postman. He gets paid for his work based on a formula: 3l(4l - 5) + 3, where l is the number of letters he delivers. If he delivers 5 letters on Monday, then how much (in Rs.) will he get paid for it?

Katie makes two rectangular boxes. One box has a length, breadth and height of 5a, 3a² and 7a⁴, respectively, while the other box has a length, breadth and height of xy, 2x²y and 2xy², respectively. Now, she joins them together to make a new rectangular box. Find the volume of the new box.

Sumit opens a new account in ABS bank. In the first month, he deposits amount p in his account. In the second month, he deposits amount p² in his account. In the third month, he deposits thrice the amount deposited by him in the first month. In the fourth month, he deposits an amount equal to the product of amounts deposited by him in the last three months. Find the amount deposited by him in the fourth month.

A tortoise and a rabbit were having a race. For every (k(k - j) + j(j - h)) kilometres covered by the tortoise, the rabbit covered three times that distance and an extra h(h - k) kilometres. Find the distance travelled by the rabbit for every (k(k - j) + j(j - h)) kilometres covered by the tortoise.

Directions: Study the following statements and choose the correct option accordingly.

Statement I: The product of (8p² + 5q) and (8p² + 5q) at p = 2 and q = 3 is 541.
Statement II: The value of is 7.

Match the following:

If p² + q² = 26 and pq = 5, then find the values of:

(i) p + q, (ii) p - q, (iii) p⁴ + q⁴

Choose the correct option from below:

	(i)	(ii)	(iii)
A	6	4	626
B	6		864
C		4	745
D	6	4	563

Fill in the blanks:
(i) Monomial is an algebraic expression consisting of ____P____ non-zero term(s) only.
(ii) A monomialin variable x is an expression of the form CX^k, whereC is a ______Q____ and k is a non-negative integer.
(iii) Any two polynomials can be added, subtracted or multiplied, and the result will be a _____R_____.
(iv) Terms, _____S_______, and coefficients make up mathematical expressions.

Choose the correct option from below:

Simplify the following:

=