(a + b)^2 Expansion and Visualisation

Q.

On factorising $3m^2+9m+6$, we get the factor(s) as:

1. 3

2. m+2

3. m+3

4. All the above

Q.

Solve${(2x+3y)}^5$ using binomial theorem

Q.

What is the value of $\sqrt{10+\sqrt{25+\sqrt{108+\sqrt{154+\sqrt{225}}}}}$ =?

1. 6

2. 4

3. 8

4. 10

Q.

Find the value of $\frac{1}{2}\sqrt{486}-\sqrt{\frac{27}{2}}$

Q.

Which of the following is a factor of $x^2+6x+9$?

1. 8 - x

2. x - 2

3. x - 6

4. x + 8

Q.

Simplify: ${\left(4m+5n\right)}^2+{\left(5m+4n\right)}^2$.

Q.

Question 77

How many times of 30 must be added together to get a sum equal to ${30}^7$?

Q.

If $a-b=2$ and $ab=48$, find the value of $a^2+b^2$.

1. $100$

2. $150$

3. $0$

4. $50$

Q.

Question 3 (v)

Subtract:

$-m^2+5mnfrom4m^2-3mn+8$

Q.

The factors of $x^4+y^4+x^2{y}^2$ is

1. $(x^2+y^2)(x^2+y^2–xy)$

2. $(x^2+y^2)(x^2–y^2)$

3. $(x^2+y^2+xy)(x^2+y^2–xy)$

4. Factorisation is not possible

Q.

Use a suitable identity to get each of the following products.

$\left(6x-7\right)\left(6x+7\right)$

Q. Factorise $a^2+8a+16$

1. $(a+4{)}^2$
2. $(a-4{)}^3$
3. $(2a-1{)}^2$
4. $(a-4)(a+4)$

Q.

The sum of the squares of two natural numbers is $34$. If the first number is one less than twice the second number, find the numbers.

Q.
What is the minimum integral value of x such that both a and b are equal to x and the flow doesn't pass through "Add 1 to a and 1 to b" before the termination of the process?

1. 4
2. 5
3. 7
4. 6

Q.

Find the value of

$\left(i\right){81}^{\frac{1}{3}}\times {576}^{\frac{1}{3}}$

$\left(ii\right){64}^{-\frac{2}{3}}\times {27}^{-\frac{2}{3}}$

Q.

Factorise: $18x^3{y}^3-27x^2{y}^3+36x^3{y}^2$

1. $9x^2{y}^2(2xy-3y+4x)$

2. $9x^2{y}^2(2xy+3y+4x)$

3. $9x^2{y}^2(2xy-3y-4x)$

4. $9x^2{y}^2(2xy+3y-4x)$

Q. Factorise $25m^2+30m+9$

1. $(m+3)(5m+2)$
2. $(m-3)(5m+2)$
3. $(5m-3{)}^2$
4. $(5m+3{)}^2$

Q.

If $a<0,$ the function $(e^{ax}+e^{-ax})$is a decreasing function for all values of x, where

1. $x<0$

2. $x>0$

3. $x<1$

4. $x>1$

Q. If $a+b+c$ = 9 and $ab+bc+ca=26$, then the value of $a^3+b^3+c^3-3abc$ is:

1. 27
2. 729
3. 29
4. 495

Q.

Factorise: $2ax+2bx-ay-by$

1. (a + b) (x + y)

2. (a - b) (x - y)

3. (a + b) (x - y)

4. (a - b) (x + y)

Q. If $(x^2+\frac{1}{x^2})=102$, then find the value of $(x+\frac{1}{x})$.

Q. If $x-\frac{1}{x}=5$, find the value of $x^2+\frac{1}{x^2}$ and $x^4+\frac{1}{x^4}$.

1. $x^2+\frac{1}{x^2}=27,x^4+\frac{1}{x^4}=727$
2. $x^2+\frac{1}{x^2}=27,x^4+\frac{1}{x^4}=731$
3. $x^2+\frac{1}{x^2}=23,x^4+\frac{1}{x^4}=527$
4. $x^2+\frac{1}{x^2}=23,x^4+\frac{1}{x^4}=531$

Q. Verify the identity ${(a+b)}^2\equiv a^2+2ab+b^2$ geometrically by taking $a=3$ and $b=2$

Q. Find the value of $x^2+\frac{1}{x^2}$, if $x+\frac{1}{x}=\sqrt{3}$

1. $-1$
2. $1$
3. $2$
4. $4$

Q. Simplify: ${(2pq+2qr)}^2-8p{q}^{2}r$

1. $4p^2{q}^2-4q^2{r}^2$
2. $4p^2{q}^2+4q^2{r}^2$
3. $4p{q}^2+4q^2{r}^2$
4. $4p^2{q}^2+9q^2{r}^2$

Q.

$63a^2-112b^2$. How do we factorize this using a suitable identity?

1. $7(3a–4b)(3a+4b)$

2. $7(3a+b)(a–4b)$

3. $(3a–4b)(3a–4b)$

4. $(3a–4b)(3a+4b)$

Q.

When we factorise $y^2+xy+yz+xz$, one of the factors is _____________

1. 1/2(x²+2x+3)

2. 1/2

3. (x²+2x+3)

4. 1

Q.

$7x^3+42=1554$. Find the value for x. [3 MARKS]

Q.

Solve The Equation $5^{2x}-24\times 5^x-25=0$ Find The Roots.

Q.

Factorise: $ax+bx+ay+by$

1. $(x+a)(y+b)$

2. $(x+b)(y+a)$

3. $(x+y)(a+b)$

4. $(x+a+b)\left(y\right)$