Expansion of (a + b)^2

Q.

What is the eigenvalue equation?

Q. In the expansion of $(5x-3)(x+2{)}^2$ ; find the coefficient of $x$.

1. 5
2. 8
3. 20
4. -12

Q. The value of $\sqrt{6+2\sqrt{5}}-1$ is .

1. 1
2. 0
3. $\sqrt{5}$

Q. If the value of $a+\frac{1}{a}=3$, then the value of $a^4+\frac{1}{a^4}$ is equal to.

1. 45
2. 47
3. 49
4. 51

Q. The length of the rectangle is $(4ab+6)m$ and breadth of the rectangle is $(6b^2+2ab)m$. Find the area of the rectangle.

1. $(24a{b}^3+18a^2{b}^2+36b^2+12ab)m^2$.
2. $(24a{b}^3+6a^2{b}^2+6b^2+12ab)m^2$
3. $(24a{b}^3+8a^2{b}^2+36b^2+12ab)m^2$
4. $(8a^2{b}^2+36b^2+ab)m^2$.

Q. If the area of the rectangle is $9x^2-12x-32$, then find out the perimeter of the rectangle.
[4 Marks]

Q. If $(a+b)=7$ and $ab=12$, then .

1. $(a-b)=\pm 1$
2. $(a-b)=\pm 2$
3. $(a-b)=\pm 3$
4. $(a-b)=\pm 4$

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. Expand each of the following , using suitable identities :
${(3a-7b-c)}^2$

Q. Factorize the given equation by grouping method $(2a-b{)}^2-10a+5b$

1. $(2a-b)(2a+b-5)$
2. $(2a-b)(2a-b+5)$
3. $(2a-b)(2a-b-5)$
4. $(2a+b)(2a-b-5)$

Q.

If $3a+5b+4c=0$, show that:
$27a^3+125b^3+64c^3=180abc$.

Q. The value of (52)${}^2$ is:

Q.

If $a=3$ and $b=2$, find :

$ab$

Q.

What is $-35023+847$?

Q. If $x=3$ and $y=-1$, find the values of each of the following using in identity:
$(\frac{3}{x}-\frac{x}{3})(\frac{x^2}{9}+\frac{9}{x^2}+1)$