Simplification of Expressions

Q. The length of a rectangle is four times its breadth. Find the simplified expression for the perimeter and the area of the rectangle.
( $l$ = Length of the triangle, $b$ = Breadth of the triangle)

1. Perimeter $=5b$ units
   Area $=4b^2$ square units
2. Perimeter $=10b$ units
   Area $=5b^2$ square units
3. Perimeter $=10b$ units
   Area $=4b^2$ square units
4. Perimeter $=4b^2$ units
   Area $=10b$ square units

Q. If the sum of three consecutive natural numbers starting from $x$ is $21,$ find the simplified algebraic expression for the sum and also find all the three numbers.

1. Simplified expression for sum $=3x+3$
   Three consecutive natural numbers $=6,7$ and $8$
2. Simplified expression for sum $=3x+2$
   Three consecutive natural numbers $=7,8$ and $9$
3. Simplified expression for sum $=3x+1$
   Three consecutive natural numbers $=9,10$ and $11$
4. Simplified expression for sum $=3x+3$
   Three consecutive natural numbers $=8,9$ and $10$

Q. Simplify:

$\left(ii\right)$. $4a+3b-2a-b$

Q.

Add the terms: $-2abc,3abc,abc$

Q. Which among the following expression after simplification would contain only $3$ terms?

1. $21x+32y+2x-27y+5y$
2. $5x+6y-4x-y$
3. $3x+y+2x$
4. $9x+7y+7x+9y+8$

Q. Simplify and match the followings:

1. $12x^2$
2. $2a{b}^3$
3. Can't simplify

Q.

Add the terms: $2abc,3bacand7cab$

Q.

Add the terms: $7x$, $-3x$.

Q. Simplify the expression: $5+7x\left[3\right(4x+9)+8]$

1. $x^2+245x+5$
2. $84x^2+245x$
3. $84x^2+250x$
4. $84x^2+245x+5$

Q. Solve: $3(x+5y)-6x-8y$

1. $3y-7x$
2. $7y-3x$
3. $7y-3y$
4. $7x-3x$

Q. For the expression $6x^5{y}^2$, choose the appropriate pairs.

1. $6x^5{y}^2$
2. Exponent of $x$
3. Variables are
4. Exponent of $y$
5. $5$
6. $2$
7. $xandy$
8. $6\times x^5{y}^2$

Q.

Subtract $0$ from $2{\mathrm{a}}^2+3\mathrm{a}+4$

Q. Match the following:

1. Like terms
2. Unlike terms
3. Unlike terms

Q.

Add the following : $x+y+z$

Q.

Find the sum $(w-7)+(-6w-5)$

Q. For the simplified form of the expression $2a+3b-4a+6b+2a-9b,$ which of the following statements is correct?

1. Contains only variable "$a$"
2. Contains only variable "$b$"
3. A constant term
4. Zero

Q. Write in simple form:
$(14x^{1000}+20x^{10}{y}^5+3y^{1000})+(-2y^{1000}-10x^{10}{y}^5+x^2-14x^{1000})$

1. $30x^{10}{y}^5+5y^{1000}+x^2$
2. $10x^{10}{y}^5+y^{1000}+x^2$
3. $10x^{10}{y}^5+5y^{1000}+x^2$
4. $30x^{10}{y}^5+y^{1000}+x^2$