algebra

Question 1

What is the identity for (a + b)²?

Answer 1

a² + 2ab + b²

This identity expands the square of a binomial.

Question 2

What is the identity for (a - b)²?

Answer 2

a² - 2ab + b²

This identity shows the square of the difference of two terms.

Question 3

What is the difference of squares identity?

Answer 3

a² - b² = (a + b)(a - b)

This identity represents the factorization of the difference of two squares.

Question 4

What is the identity for (a + b)³?

Answer 4

a³ + b³ + 3ab(a + b)

This identity expands the cube of a sum.

Question 5

What is the identity for (a - b)³?

Answer 5

a³ - b³ - 3ab(a - b)

This identity expands the cube of a difference.

Question 6

Fill in the blank: a + b³ = _______

Answer 6

(a + b)(a² - ab + b²)

This is a form of the identity for the sum of cubes.

Question 7

Fill in the blank: a - b³ = _______

Answer 7

(a - b)(a² + ab + b²)

This is a form of the identity for the difference of cubes.

Question 8

What is the identity for (a + b + c)²?

Answer 8

a² + b² + c² + 2ab + 2bc + 2ca

This identity represents the square of a trinomial.

Question 9

What is the identity for a³ + b³ + c³ - 3abc?

Answer 9

(a + b + c)(a² + b² + c² - ab - ac - bc)

This identity is useful in factoring cubic expressions.

Question 10

If a + b + c = 0, what is the identity for a³ + b³ + c³?

Answer 10

3abc

This simplifies the expression when the sum of the variables is zero.

Question 11

What is the identity for a⁴ - 64?

Answer 11

(a + 4)(a - 4)(a² + 16)

This represents the factorization of a difference of squares with a fourth power.

Question 12

Fill in the blank: a³ + a² + 1 = _______

Answer 12

(a² + 1)² - a

This identity is a rearrangement that highlights a squared term.