Simplification of an Expression

Q.

Solve the following equation and check your results: $4z+3=6+2z$

Q.

If $2x=3+5i$, then the value of $2x^3+2x^2-7x+72$ is

1. $4$

2. $-4$

3. $8$

4. $-8$

Q.

Evaluate ${\left(99\right)}^3$ using suitable identities

Q. Using arithmetic identity find the square of 87.

Q. Find the square of 101 using an appropriate algebraic identity.

1. 10001
2. 10201
3. 10101
4. 20102

Q. Expand :
${[\sqrt{3x}-\frac{\sqrt{2}}{5}y]}^2$

1. $3x^2-\frac{2}{5}\sqrt{6x}+\frac{2}{25}$
2. $3x-\frac{2\sqrt{6x}y}{5}+\frac{2}{25}{y}^2$
3. $3x^2-\sqrt{6x}+\frac{4}{25}$
4. $x^2-\frac{2}{5}\sqrt{6x}+\frac{4}{25}$

Q.

Evaluate the following without actual multiplication : ${\left(72\right)}^2$

Q.

Question 84 (c)

Simplify and express each of the following in exponential form.
$(3^7÷3^5{)}^4$

Q.

Find the square of $395$ using identity

Q. If $x-\frac{1}{x}=-1$. Find value of $x^2+(\frac{1}{x}{)}^2$.

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

Q.

Find the following squares by using the identities ${(6x^2–5y)}^2$.

Q. If $\frac{3}{5}x+9=33$, what is the value of $x$?

1. 20
2. -20
3. -40
4. 40

Q.

$1c{m}^2=.......m{m}^2$

Q. Question 6(ix)
Using identities, evaluate:
$1.05\times 9.5$

Q.

Simplify :

$2a-\left[4b-\left\{4a-(3b-\overline{2a+2b}\right\}\right]$

Q. Question 3
5x + 9 = 5 + 3x

Q.

$3a-[4a-\overline{3a-5b}-3${$2a-(3a-\overline{2a-3b})$}$]$ equals

1. $-a-14b$

2. $5a-14b$

3. $5a+14b$

4. $-a+14b$

Q.

Question 44

State whether the following statement is true (T) or false (F).

If 6x=18, then 18x=54.

Q. $\text{If}{35}^2-{27}^2=8a,$
$\text{then find the value of a.}$

1. 62
2. 52
3. 42
4. 56

Q. $\text{If}a=6p\text{and}b=3p,$
$\text{then find the expansion of}$
$(a+b{)}^2+(a-b{)}^2.$

1. $72p^2-18q^2$
2. $72p^2+18q^2$
3. $18p^2+72q^2$
4. $18p^2-72q^2$

Q. Simplify the following expressions
$(5+\sqrt{7})(2+\sqrt{5})$

Q. $\text{If}a=6p\text{and}b=3p,$
$\text{then find the expansion of}$
$(a+b{)}^2+(a-b{)}^2.$

Q. Solve the expression using BODMAS rule: $3x(x-2)+x(x^2\times 2x)-12x$

1. $2x^5-3x^2-18x$
2. $2x^5+3x^2-18x$
3. $2x^5+3x^2+18x$
4. $-2x^5-3x^2-18x$

Q.

$-2(1-m^2)-4\{m^2-(2-m^2\left)\right\}$=______.

1. $6m^2+6$

2. $-6m^2-6$

3. $6m^2+6$

4. $-6m^2+6$

Q. Verify that $x^3+y^3+z^2-3x{y}^2=\frac{1}{2}(x+y+z)[{(zx-y)}^2+{(y-z)}^2+{(z-x)}^2]$

Q.

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

1. 1/2(x²+2x+3)

2. 1/2

3. (x²+2x+3)

4. 1

Q. Simplify each of the following products:
$(\frac{x}{2}-\frac{2}{5})(\frac{2}{5}-\frac{x}{2})-x^2+2x$

Q. The famous Shakesperean phrase "To be or not to be" gives the output "Gb or be abg gb or" when entered into a machine that creates codes. If the name "William Shakespeare" was the input, what would be the output?

"Gb or be abg gb or"

Q. Express as a power of a rational number with positive exponent $8^6\times 8^{-5}$

Q. Divide :
(i) $9m^5+12m^4-6m^{2}by3m^2$
(ii) $24x^{3}y+20x^2{y}^2-4xyby2xy$