Multiplication of Polynomials

Q.

Question 82 (ii)

Subtract

$6x^2-4xy+5y^{2}from8y^2+6xy-3x^2$

Q.

$(x+y)(x-y)(x^2+y^2$) is equal to

1. ( + )

2. x⁴ - y⁴

3. ( - )

4. x³ + y³

Q. Multiply $x^3+10x^2-2$ by (x +1)

1. $x^4-11x^3+10x^2-2x-2$
2. $x^4+11x^3+10x^2+2x-2$
3. $x^4+11x^3+10x^2-2x-2$
4. $x^4+11x^3-10x^2-2x-2$

Q. If the area of the rectangle is $9x^2-12x-32$, then the perimeter of the rectangle is .

1. $2(3x-10)(3x+2)$
2. $2(3x+10)(3x-2)$
3. $2(6x-4)$

Q. The value of $\frac{3^2+4^2+5^2+24+40+30}{3+4+5}$ is :

1. 12
2. 42
3. 24
4. 21

Q. The length of a rectangular field is two more than twice its breadth. Find its area if the breadth is x + 1?

1. $2x^2+6x+4$
2. $2x^2+3x+2$
3. $x^2+6x+2$
4. $x^2+8x+24$

Q.

$(a+b+c)(a+b-c)$ = ___.

1. a²+4ab+b²-c²

2. a²+2ab+b²

3. a²+2ab-c²

4. a²+2ab+b²-c²

Q.

Question 81 (iv)

Add :

$5x^2-3xy+4y^2-9,7y^2+5xy-2x^2+13$

Q.

Subtract the following:$(14a^{3}b-10b^2-28a){\text{from (20a}}^3{\text{b+11b}}^2\text{+15a)}$

Q. Multiply $(x^3+10x^2-2)$ by $(x+1)$.

1. $x^4+11x^3-10x^2-2x-2$
2. $x^4-11x^3+10x^2-2x-2$
3. $x^4+11x^3+10x^2-2x-2$
4. $x^4+11x^3+10x^2+2x-2$

Q.

Simplify: $(3x-2y)(3x+4y)-(3x+2y)(3x-2y)$

1. $0$

2. $-4y^2+6xy$

3. $2y(-2y+3x)$

4. Both B and C

Q.

The value of $(3x^2+5y^2)(4xy-5y)$, if $x=2$ and $y=3$ is $513$.

1. False

2. True

Q.

Unlike terms can be _______.

1. added

2. multiplied

3. subtracted

4. both added and subtracted

Q. multiple$A=\frac{{3x}^4}{4}-\frac{x^4}{2}+5x-7;B=\frac{{2x}^3}{3}+\frac{{3x}^3}{2}-\frac{x}{6};C=\frac{{2x}^4}{3}-\frac{{3x}^4}{4}+5$ find
$3A-2B-C$

Q.

If $z=\left|\begin{array}{ccc}1& 1+2i& -5i\\ 1-2i& -3& 5+3i\\ 5i& 5-3i& 7\end{array}\right|$, then

1. $z$ is purely real

2. $z$ is purely imaginary

3. $z-\overline{z}=0$

4. $z-\overline{z}$ is purely imaginary

Q. Find the product of the following binomials :

(i) $(\frac{4}{3}{x}^2+3)(\frac{4}{3}{x}^2+3)$

Q. Which of the following is the correct expansion of the given identity?
$(x+a)(x+b)$

1. $x^2+(a+b)x+ab$
2. $x^2-(a+b)x+ab$
3. $x^2+(a+b)x-ab$
4. $x^2-(a+b)x-ab$

Q.

If the length and breadth of a rectangle are $(x^2-x+2)$ cm and $(x^2+x-2)$ cm respectively, find the area of the rectangle.

1. $x^4-5x^3-x^2$

2. $x^4-x^3-4x^2+4$

3. $x^4-x^3-x^2-4x$

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

Q.

The value of $(3x^2+5y^2)(4xy-5y)$, if $x=2$ and $y=3$ is $513$.

1. False

2. True

Q.

Expand: ${(7x+8y)}^3$

Q. Which of the following is the correct expansion of the given identity?
$(a-b{)}^2$

1. $a^2-2ab+b^2$
2. $a^2-2ab-b^2$
3. $a^2+2ab+b^2$
4. $a^2+2ab-b^2$

Q. Simplify
${(x-2y+3)}^2+{(x+2y-3)}^2$

Q.

Multiply $(7x-4x^2+2x^3-5)$ with $(3x-2)$.

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

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

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

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

Q.

If base and the altitude of a triangle are $(3m+2n)$ and $(3m-4n)$ repectively, then the area of the triangle is _____.

1. $\frac{1}{2}\times (9m^2+6mn-8n^2)$

2. $\frac{1}{2}\times (9m^2-6mn+8n^2)$

3. $\frac{1}{2}\times (9m^2-6mn-8n^2)$

4. $\frac{1}{2}\times (9m^2+6mn+8n^2)$

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.

The product of $(x+7y)and(7x-y)$ is

1. $7x^2-48xy-7y^2$

2. $7x^2-48xy+7y^2$

3. $7x^2+48xy+7y^2$

4. $7x^2+48xy-7y^2$

Q.

$(a+b+c)(a-b-c)$ = ______

1. $a^2+b^2-c^2-ca$

2. $a^2-b^2+c^2-2ca$

3. $a^2+b^2+c^2-bc$

4. $a^2-b^2-c^2-2bc$

Q.

Unlike terms can be _______.

1. multiplied

2. both added and subtracted

3. subtracted

4. added

Q.

$(a+b+c)(a-b-c)$ = ______

1. $a^2+b^2-c^2-ca$

2. $a^2-b^2+c^2-2ca$

3. $a^2+b^2+c^2-bc$

4. $a^2-b^2-c^2-2bc$

Q. Which of the following is the correct expansion of the given identity?
$(a^2-b^2)$

1. $(a+b)(a-b)$
2. $(a+b)(a+b)$
3. $(-a+b)(a-b)$
4. $(a+b)(-a-b)$