Explanation

(√x + √y) (√x - √y)

= (√x)² - (√y)²

= x - y

Explanation

x² - xy + y²

= (-2)² - (-2)(2) + (2)²

= 4 + 4 + 4

= 12

Explanation

(3a - 2b)² = (3a)² - 2(3a)(2b) + (2b)²

= 9a² - 12ab + 4b²

Explanation

The expression x² + 7x + 3 has three terms.

A polynomial with three terms is called a trinomial.

Explanation

a² - b² = (a - b)(a + b).

Explanation

a + b = 2 ... (1)

a - b = 2 ... (2)

Adding (1) and (2):

2a = 4

a = 2

Put a = 2 in (1):

2 + b = 2

b = 0

Now, a² + b² = (2)² + (0)² = 4 + 0 = 4.

Explanation

In the Cartesian coordinate system:

• 1st quadrant: (+, +)
• 2nd quadrant: (-, +)
• 3rd quadrant: (-, -)
• 4th quadrant: (+, -)

Given P(2, -3), the x-coordinate is positive (+) and the y-coordinate is negative (-), so it lies in the 4th quadrant.

Explanation

n(A × B) = n(A) × n(B) = 3 × 4 = 12.

Explanation

Positive sign (+) indicates profit, so +5 means profit of Rs. 5.

Negative sign (−) indicates loss, so −5 means loss of Rs. 5.

Explanation

A right bisector of a line segment is a line that cuts it into two equal parts at 90°.

It always passes through the midpoint of the segment.