Special Products

In algebra, _____ are a few common patterns that emerge when multiplying polynomials. Recognizing these patterns simplifies multiplication and factoring.

• special products

• expression

• inner terms

In the problem x + 4 𝑥 + 4 , we are multiplying the same _____ by itself, which means that we are squaring the _____. This means that:

(x + 4)(x + 4) = (x +4)^2

= x^2 + 4x + 4x + 16

= x^2 + 8x + 16

• special products

• expression

• inner terms

Since the product of the _____ is the same as the product of the outer terms, we can simplify the solution to similar problems using the patterns below:

(x + y)^2 = x^2 + 2xy^2 + y^2

(x - y)^2 = x^2 - 2xy + y^2

• special products

• expression

• inner terms

The _____ of the product is always the square of the _____ in the binomial.

• first term

• middle term

• last term

The _____ of the product is always twice the product of the two terms in the binomial.

• first term

• middle term

• last term

The _____ of the product is always the square of the _____ in the binomial.

• first term

• middle term

• last term

(5m - 1)^2

(a + 7)^2

Cube of a Binomial, as the name suggests, is the third power of any binomial expression.
Cube of a Binomial follows a specific formula, which is:
(x + y)^2 = x^3 + 3x^2y + 3xy^2 + y^3

(x - y)^2 = x^3 - 3x^2y + 3xy^2 - y^3

• Cube of a Binomial

• First term

• Second term

• Third term

• Fourth term

(x + y)^2 = x^3 + 3x^2y + 3xy^2 + y^3

(x - y)^2 = x^3 - 3x^2y + 3xy^2 - y^3
_____: The cube of the _____ of the binomial.

• Cube of a Binomial

• First term

• Second term

• Third term

• Fourth term