Explanation

Given the expression a² - 2a + 1 - b²:

Step 1: Factor the perfect square trinomial

a² - 2a + 1 = (a - 1)²

So, the expression becomes (a - 1)² - b²

Step 2: Apply the difference of squares formula

(a - 1)² - b² = (a - 1 - b)(a - 1 + b)

Explanation

To expand the expression:

(√3 - √2)²

= (√3)² - 2(√3)(√2) + (√2)²

= 3 - 2√6 + 2

= 5 - 2√6

Explanation

When two lines intersect, they form four angles around the intersection point.

The sum of these four angles is always 360°, as they complete a full circle.

Explanation

George Cantor, a German mathematician, is known as the father of set theory.

He introduced the concept of infinite sets and their cardinalities in the late 19th century.

Explanation

Factors of 4 = 1, 2, 4

Factors of 6 = 1, 2, 3, 6

Factors of 8 = 1, 2, 4, 8

Highest Common Factor (H.C.F) = 2 (common to all three numbers)

Explanation

A chord is a line segment with both endpoints on the circle.

If it does not pass through the center, it's simply a chord.

Explanation

Sets that have the same number of elements (cardinality) are called equivalent sets.

They may have different elements but the same total count.

Explanation

A cuboid is a 3D solid shape bounded by six rectangular faces.

Opposite faces of a cuboid are equal and each angle is a right angle.

Explanation

8.0560 has 5 significant figures: 8, 0, 5, 6, and the final 0 (after decimal) is also significant.

Trailing zeros after a decimal point are always significant.

Explanation

We want the least number of stickers that can be equally divided among 4, 10, and 16 children.

This means we want the Least Common Multiple (LCM) of 4, 10, and 16.

The prime factorizations are:

4 = 2²

10 = 2 × 5

16 = 2⁴

The LCM is the product of the highest powers of all prime factors:

LCM = 2⁴ × 5 = 16 × 5 = 80