Explanation

The given expression is:

a³ + 3ab(a + b) + b³

Factor the expression:

(a + b)(a² - ab + b²) + 3ab(a + b)

Combine like terms:

(a + b)(a² - ab + b² + 3ab)

Simplify:

(a + b)(a² + 2ab + b²)

Recognize the perfect cube:

(a + b)³

Explanation

Given:

x + (1/x) = 8

Cube both sides:

(x + (1/x))³ = 8³

Expand the left side:

x³ + 3x²(1/x) + 3x(1/x)² + (1/x)³ = 512

Simplify:

x³ + 3x + 3(1/x) + (1/x)³ = 512

Rearrange:

x³ + (1/x)³ + 3(x + (1/x)) = 512

Substitute x + (1/x) = 8:

x³ + (1/x)³ + 3(8) = 512

x³ + (1/x)³ + 24 = 512

Subtract 24 from both sides:

x³ + (1/x)³ = 488

Explanation

Explanation

Explanation

A metaphor directly compares two unrelated things without using "like" or "as" — here, life is directly called a box of chocolates.

It implies that life is full of surprises, just like assorted chocolates in a box.

Explanation

To round off 87.321756 to 5 significant figures, we look at the 6th significant figure, which is 6.

Since it's greater than 5, we round up the 5th significant figure.

87.321756 becomes 87.322

Explanation

Idealism focuses on the essence or true nature of things, believing that ideas and mental constructs are the highest reality.

It holds that universal truths exist beyond physical matter and particular qualities.

Explanation

The Discussion method encourages learners to list key points, raise questions, and explore ideas from readings or experiences.

It promotes critical thinking, engagement, and active participation in the classroom.

Explanation

The formula for the sum of interior angles of a polygon is:

(n - 2) × 180°

For an 8-sided polygon (n = 8):

Sum of interior angles = (8 - 2) × 180°

= 6 × 180°

= 1080°

Since it's a regular polygon, all interior angles are equal:

Measure of each interior angle = 1080°/8

= 135°

Explanation

A point source of pollution refers to a fixed or stationary location, like a factory chimney or wastewater outlet.

It contrasts with mobile sources (like vehicles) or diffuse sources (like agricultural runoff).