Question

4. Let's find the squares of the following expressions (i) by geo

(ii) without using formula (iii) using formula.
a) (x + 1)
b) (x + 2)

Answer 1

To find the squares of the expressions (x + 1) and (x + 2), you can use geometric representation, expand the expressions without using formula, or use the formula (a + b)². Each method has its own benefits and can help in understanding the concept of squaring.

Step-by-step explanation:

(i) By using geometric representation:

1. a) (x + 1):
2. To find the square of (x + 1) geometrically, we can draw a square with side length(x + 1). Then, using the concept of area, we can calculate the square of (x + 1) as the area of the square.
3. b) (x + 2):
4. To find the square of (x + 2) geometrically, we can draw a square with side length(x + 2). Then, using the concept of area, we can calculate the square of (x + 2) as the area of the square.

(ii) Without using a formula:

1. a) (x + 1):
2. To find the square of (x + 1) without using a formula, we can expand the expression by multiplying it by itself: (x + 1)(x + 1). Then, we can simplify the expression by using the distributive property and combining like terms.
3. b) (x + 2):
4. To find the square of (x + 2) without using a formula, we can expand the expression by multiplying it by itself: (x + 2)(x + 2). Then, we can simplify the expression by using the distributive property and combining like terms.

(iii) Using a formula:

1. a) (x + 1):
2. To find the square of (x + 1) using the formula, we can use the identity (a + b)² = a² + 2ab + b². In this case, a = x and b = 1. We can substitute these values into the formula and simplify the expression.
3. b) (x + 2):
4. To find the square of (x + 2) using the formula, we can use the identity (a + b)² = a² + 2ab + b². In this case, a = x and b = 2. We can substitute these values into the formula and simplify the expression.