# How to Product of algebra

Mathematical expressions are just like sentences and their parts have special names. You should be familiar with the following words used to describe the parts of mathematical expressions.

3x^{2} + 7xy – 5^{3}

**Multiplying a monomial and a binomial**

Also Read:

A monomial is an expression with one term, for example, 3x or y^{2}. A binomial is an expression with two terms, for example, ax + b or cx + d.

Example 1:

Simplify : 2a (a – 1) – 3(a^{2} – 1)

Solution:

2a (a – 1) – 3(a^{2} – 1) = 2a ( a) + 2a ( -1 ) + (-3) (a^{2} ) + ( -3) ( – 1)

2a (a – 1) – 3(a^{2} – 1) = 2a^{2} – 2a – 3a^{2} + 3

2a (a – 1) – 3(a^{2} – 1) = -a^{2} – 2a + 3

**Multiplying two binomials**

Here we multiply (or expand) two linear binomials:

(ax + b) (cx + d) = (ax) (cx) + (ax) d + b (cx) + bd

(ax + b) (cx + d) = acx^{2} adx + bcx + bd

(ax + b) (cx + d) = acx^{2} + x ( ad + bc ) + bd

Example 2 :

Find the product: (3x – 2) (5x + 8)

Solution :

(3x – 2) (5x + 8) = (3x) (5x) + (3x) (8) + (-2) (5x) + (-2) (8)

(3x – 2) (5x + 8) = 15x^{2} + 24x – 10x – 16

(3x – 2) (5x + 8) = 15x^{2} + 14x – 16

The product of two identical binomials is known as the square of the binomial and is written as:

( ax + b)^{2} = a^{2}x^{2} + 2abx + b^{2}

If the two terms are of the form ax + b and ax – b then their product is:

(ax + b) (ax –b ) = a^{2}x^{2} – b^{2}

This product yields the difference of two squares.

**Also Read : Product and quotients of monomials**

**Multiplying a binomial and a trinomial**

A trinomial is an expression with three terms, for example, ax^{2} + bx + c. Now we can learn how to multiply a binomial and a trinomial.

(A + B) (C + D + E) = A(C + D + E) + B (C + D + E)

Example 3:

Find the product: ( x – 1) ( x^{2} – 2x + 1)

Solution:

**Step 1: Expand the bracket**

( x – 1) ( x^{2} – 2x + 1) = x (x^{2} – 2x + 1) – 1 (x^{2} – 2x + 1)

( x – 1) ( x^{2} – 2x + 1) = x^{3} – 2x^{2} + x – x^{2} + 2x – 1

**Step 2: Simplify**

( x – 1) ( x^{2} – 2x + 1) = x^{3} – 3x^{2} + 3x -1