Multiplication of Any Polynomial

Q.

Multiply the following:
i) $-3x^{2}y,(5y-xy)$
ii) $7pqr,(p-q+r)$
[2 marks]
[NCERT-Exemplar-Q83(v, vii)]
[ <!--td {border: 1px solid #cccccc;}br {mso-data-placement:same-cell;}--> Multiplication ​of algebraic ​expressions]

Q.

The expression obtained by multiplying $(7x-4x^2+2x^3-5)$ with $(3x-2)$ is:

1. $6x^4-16x^3+29x^2-x+1$

2. $6x^4-16x^3+27x^2-x+10$

3. $5x^4-16x^3+29x^2-x+10$

4. $6x^4-16x^3+29x^2-29x+10$

Q.

The length of a rectangular field is one more than twice of the breadth. What is its area if the breadth is $x$?

1. 2$x^2$ - $x$

2. $2x-1$

3. $x^2$ + $2x$

4. 2$x^2$ + $x$

Q.

Unlike terms can be _______.

1. added

2. multiplied

3. subtracted

4. both added and subtracted

Q.

Find:
$(a+b+c)\times (a+b-c)=$

1. $a^2+2ab-c^2$

2. $a^2+4ab+b^2-c^2$

3. $a^2+2ab+b^2$

4. $a^2+2ab+b^2-c^2$

Q.

Simplify $(3x^2+5y^2)(4xy-5y)$.

1. $(6x^{3}y-15xy+20x{y}^3-5y^3)$

2. $(12x^{3}y-5x^{2}y+10x{y}^3+25y^3)$

3. $(12x^{3}y-15x^{2}y+20x{y}^3-25y^3)$
4. $(6x^{3}y-15x^{2}y+10x{y}^3-5y^3)$

Q.

Find the product of $(t+s^2)$ and $(t^2-s)$.

1. $t^3+s^2{t}^2-st-s^3$

2. $t^3+s^2{t}^2-st-s^2$

3. $t^3+s^2{t}^2-2st-s^3$

4. $t^3+t^2-st-s^3$

Q.

What is the result if a monomial is multiplied by a monomial?

1. Monomial

2. Trinomial

3. Binomial

4. Constant

Q.

Find the area of a rectangle whose length is $5xy$ units and breadth is $8x{y}^2$ units.

1. $40x^2$$y^3$ square units

2. $40x^2$$y^2$ square units

3. $40x{y}^3$ square units

4. $40xy$ square units

Q. If the adjacent sides of a rectangle are $(x^2-x+2)$ units and $(x^2+x-2)$ units long, find the area of the rectangle.

1. $(x^4-5x^3-x^2)$ square units
2. $(x^4-x^3-4x^2+4)$ square units
3. $(x^4-x^3-x^2-4x)$ square units
4. $(x^4-x^2+4x-4)$ square units