Algebraic Expressions and Simplifications

This video introduces a new A-Level Maths series, covering topics like factorizing algebraic expressions, simplifying surds, rationalizing denominators, expanding brackets with surds, and working with indices. The instructor uses examples to explain each concept, providing step-by-step solutions and highlighting common pitfalls. The video aims to build confidence in handling complex mathematical problems by reinforcing foundational skills and introducing advanced techniques.

What is the first topic covered in the A-Level Maths series?

• Calculus

• Algebraic Expressions

• Trigonometry

• Statistics

How can x^4 - y^4 be factorized completely?

• (x^2 - y^2)(x + y)(x - y)

• (x^2 + y^2)(x^2 + y^2)

• (x^2 + y^2)(x + y)(x - y)

• (x^2 + y^2)(x^2 - y^2)

What is the simplified form of √75 - √12?

• 5√3

• 2√3

• 3√3

• 4√3

What is the result of rationalizing the denominator of (3 - 2√5) / (√5 - 1)?

• (7/4) + (√5/4)

• (7/4) - (√5/4)

• (-7/4) - (√5/4)

• (-7/4) + (√5/4)

How can 5 / (√75 - √50) be written in the form √a + √b?

• √5 - √2

• √3 - √2

• √5 + √2

• √3 + √2

What is the conjugate of (√5 - 1)?

• √5 + 1

• √5 - 1

• 1 - √5

• 1 + √5

What is the simplified form of 5√3 - 2√3?

• 2√3

• √3

• 7√3

• 3√3

What is the simplified form of (√11 - 5)(5 - √11)?

• 10√11 + 25

• 10√11 + 36

• 10√11 - 25

• 10√11 - 36

How can 27^(2x + 1) be written in the form 3^y?

• 3^(6x + 3)

• 3^(6x + 1)

• 3^(2x + 3)

• 3^(2x + 1)

What is the value of 'a' if 243√3 = 3^a?

• 9/2

• 11/2

• 5/2

• 7/2