Examples of Squaring a Trinomial
Some examples on squaring a trinomial are,
Example 1: Given trinomial 3x2 β 2x + 5, find square of this trinomial.
Solution:
Given trinomial,
(3x2 β 2x + 5)2
Applying Distributive Property:
(3x2 β 2x + 5)(3x2 β 2x + 5)
Distributing each term
9x4 β 6x3 + 15x2 β 6x3 + 4x2 β 10x + 15x2 β 10x + 25
Combining like terms
9x4 β 12x3 + 24x2 β 20x + 25
So, square of trinomial (3x2 β 2x + 5) is (9x4 β 12x3 + 24x2 β 20x + 25)
Example 2: A rectangular garden has an area represented by the trinomial expression 2x2+7x-4. If the length of the garden is represented by (2x + 1) units, find the width of the garden.
Solution:
Area of a Rectangle is,
Area = Length Γ Width
In this case, area of rectangular garden is represented by trinomial expression (2x2 + 7x β 4), and the length is given as (2x + 1) units.
Let the width be represented by (w). So, we have:
2x2 + 7x β 4 = (2x) Γ w
Now, we can solve for (w):
2x2 + 7x β 4 = 2xw
Divide both sides by (2x):
w = (2x2 + 7x β 4)/2x
Now, simplify the expression
w = (2x + 1)(x β 4)/(2x + 1)
w = (x β 4)
So, width of garden is given by (x β 4)
Example 3: Calculate Square of Trinomial -4a2 + 3a β 1
Solution:
= (-4a2 + 3a β 1)2
Using Distributive Property
= (-4a2 + 3a β 1)(-4a2 + 3a β 1)
= 16a4 β 12a3 + 4a2 β 12a3 + 9a2 β 3a + 4a2 β 3a + 1
= 16a4 β 24a3 + 13a2 β 6a + 1
So, square of trinomial (-4a2 + 3a β 1) is (16a4 β 24a3 + 13a2 β 6a + 1)
Squaring a Trinomial
Squaring a trinomial involves multiplying a trinomial by itself. A trinomial is an algebraic expression with three terms, typically of the form a+b+c where a, b, and c represent constants or variables.
It requires multiplying the trinomial by itself using the distributive property and then simplifying the expression by combining like terms. This process is fundamental in algebra and provides an expanded form of the trinomial.
Letβs know more Trinomial Definition, How to Square Trinomial, and Different Methods of Squaring a Trinomial with some solved examples to understand better.