Algebraic Identity: (a + b)^2 = a^2 + b^2 + 2ab

Q.

What happens to the area of a square if its side is doubled?

Q.

An identity is an equality, which is true for all values of the variables in the equality.

1. True

2. False

Q.

What happens to the area of a square if its side is halved?

Q. If each side of a square is increases by 2 units, then the new area is .

1. $a^2+4a+4$
2. $a^2+4a+2$
3. $2a^2+4a+4$
4. $a^2+2a+4$

Q. $\text{The area of a square is}9x^2+12x+4.\text{What is the measure of the side of the square?}$

Q.

How can we came to know where we have to use which identity?

Q. The value of (107)${}^2$ - (93)${}^2$ is: ____.

1. 2800
2. 1008
3. 1382
4. 36482

Q. Using the algebraic identity, evaluate 41 x 41 .

1. 1681
2. 1683
3. 1691
4. 1680

Q. Simplify $(a+b{)}^2-2ab$.

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

Q.

The area of a trampoline is about $1.8\times {10}^4$ square inches.Write this number in standard form. Then represent the area of the trampoline using more-appropriate units.

Q. $1024$ plants are planted in a grid such that the number of rows is equal to the number of columns. One row and one column of plants are then sold to a customer. Find the number of plants that were sold.

1. $61$
2. $65$
3. $63$
4. $67$

Q.

Simplify the following algebraic expression: $(9pq+6r{)}^2-108pqr$

1. $81p^2{q}^2+18r^2$

2. $81p^2{q}^2+36r^2$

3. $81p^2{q}^2+36r^2-216pqr$

4. $81p^2{q}^2+18r^2-54pqr$

Q.

Question 84 (xii)

Simplify

$(pq-qr{)}^2+4p{q}^{2}r$

Q. Area of a square poster is $25$ sq ft. The length of each side will be:

1. $\pm \sqrt{25}$
2. $-\sqrt{25}$
3. $\sqrt{-25}$
4. $\sqrt{25}$

Q. Area of a square cardboard is $2.89sqft$. The length of the side of the cardboard is _____ ft and this length is ______________ number.

1. $\mathrm{1.7...},$ an irrational
2. $\mathrm{1.445....},$ an irrational
3. $1.445,$ a rational
4. $1.7,$ a rational

Q. Simplify:$x^{a+b}{x}^{b+c}{x}^{c+a}$

Q. A gardener has $1000$ saplings in his garden. Find the minimum number of additional saplings he needs to plant in such a way that the number of rows and the number of columns of saplings remain the same.

1. $39$
2. $32$
3. $31$
4. $24$

Q. $(a+b{)}^2-(a-b{)}^2=$_______.

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

Q. Simplify:$a^2+b^2+c^2+2ab+2bc+2ca$
[2 marks]

Q.

If $x\ne 0$ and $x+\frac{1}{2x}$ = 4, then find the value of $x^2+\frac{1}{4x^2}$

1. 20

2. 15

3. 10

4. 5

Q. Simplify the given algebraic expression:
$n^2(n-2)+2n^3(n+3)-6n(n-4)$

Q. Area of a rectangle is the same as the area of a square. If the rectangle is of measurement 25 in × 14 in, find the approximate (nearest tenth) length of each side of the square.

1. 19.7 in
2. 18.4 in
3. 19.0 in
4. 18.7 in

Q. The simplification of the expression $(8x+3y{)}^2$ is .

1. $32x^2+9y^2+24xy$
2. $32x^2+9y^2+48xy$
3. $64x^2+9y^2+48xy$
4. $64x^2+9y^2+24xy$

Q.

$5x-2y=7andxy=2$, find the value of $(5x+2y{)}^2$

1. 129

2. 127

3. 145

4. 133

Q. Rock wants to paint a square wall of area $225$ square feet. What is the length of the wall?

Q.

${(4pq+3q)}^2-{(4pq-3q)}^2=$ ____________.

1. $48p{q}^2$

2. $48p^{2}q$

3. $44p^{2}q$

4. $44p{q}^2$

Q. Area of a square carpet is 1.44 sq ft. What is the length of each side of the carpet?

1. 0.36 ft
2. 1.2 ft
3. 0.72 ft
4. 12 ft

Q.

A square is of side $3\frac{3}{4}\mathrm{m}$. Find the area?

Q.

In a class, there are 529 students who are arranged in rows and columns to form a square for a P.T display. Now the teacher wants to add one more row and column for which 60 more students volunteer. Find the number of students who will not be a part of the P.T display.

1. 13

2. 20

3. 17

4. 19

Q. $\text{The area of a square is}9x^2+12x+4.\text{What is the measure of the side of the square?}$