# Perfect Square Trinomial Formula (2023)

## 1. Perfect Square Trinomial Definition - Cuemath

• A perfect square trinomial is defined as an algebraic expression that is obtained by squaring a binomial expression. It is of the form ax2 + bx + c. Here a, b, ...

• Perfect square trinomials are algebraic expressions with three terms got by multiplying a binomial with itself. Learn about its definition, pattern, method of factorization, formulas, and examples.

## 2. Perfect-Square Trinomials - Purplemath

• The trick to seeing this pattern is really quite simple: If the first and third terms are squares, figure out what they're squares of. Multiply those things, ...

• Demonstrates how to recognize perfect-square trinomials, and shows how to convert them to squared-binomial form.

## 3. Perfect Square Trinomial – Explanation & Examples

• An expression is said to a perfect square trinomial if it takes the form ax2 + bx + c and satisfies the condition b2 = 4ac. The perfect square formula takes the ...

• A quadratic equation is a second degree polynomial usually in the form of f(x) = ax2 + bx + c where a, b, c, ∈ R, and a ≠ 0. The term ‘a’ is referred to as

## 4. Perfect Square Trinomial: Definition, Formula & Examples - Study.com

• Nov 22, 2021 · For example, take the binomial (x + 2) and multiply it by itself (x + 2). (x + 2)(x + 2) = x2 + 4x + 4. The result is a perfect square trinomial ...

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## 5. 4.5 Factoring a Perfect Square Trinomial – Math 3080 Preparation

• A perfect square trinomial is a trinomial that can be written as the square of a binomial. Recall that when a binomial is squared, the result is the square of ...

## 6. Factoring perfect square trinomials (article) - Khan Academy

• if the answer is the first-degree variable coefficient (6) then it satisfy the perfect squares "trick" rule, and the answer would be (x+3)^2. when you have a ...

• Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

## 7. How to factor perfect square trinomials - StudyPug

• Factoring perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2.

• Perfect square trinomials have a common pattern, which can be factorized faster if you can recognize them. Learn how and try it out with our practice problems.

## 8. How do you factor a perfect square trinomial? - Homework.Study.com

• A perfect square trinomial will always have the form a2 + 2ab + b2. To factor a perfect square trinomial, we use the following formula:.

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## FAQs

### What is the formula for a perfect square trinomial? ›

A perfect square trinomial has three terms which may be in the form of (ax)2+ 2abx + b2= (ax + b)2 (or) (ax)2−2abx + b2 = (ax−b)2.

What is an example with answer in perfect square trinomial? ›

A perfect square trinomial will have one squared factor. They are always in the form a²+2ab+b² or a²-2ab+b². For example, x²+4x+4 = (x+2)².

Is 4x 2 12x 9 a perfect square trinomial? ›

4x 2 + 12x + 9 is a perfect square trinomial.

What completes this expression to make it a perfect square trinomial x2 4x ___? ›

The number that should be added to the expression x2+4x to change it into a perfect square trinomial is 4.

What are the rules for a perfect square? ›

A number is a perfect square (or a square number) if its square root is an integer; that is to say, it is the product of an integer with itself. A number that is a perfect square never ends in 2, 3, 7 or 8. If your number ends in any of those numbers, you can stop here because your number is not a perfect square.

Is 16x 2 24x 9 a perfect square? ›

Hence, we can say that \$16{x^2} + 24x + 9\$ is a perfect square trinomial, and the factors are \$4x + 3\$. Note: In this equation the factor is \$4x + 3\$, there is no other factor in this equation because when the given factor multiplied by itself gives the perfect square trinomial equation.

Is x2 4x 16 a perfect square trinomial? ›

∴ It is not a perfect square. (vi) x2−4x+16=(x)2−x×4+(4)2=a−ab+b2[Taking x=a, and 4=b]∴ The given trinomial cannot be expressed asa2−2ab+b2.

Is this a perfect square trinomial x2 4x 4? ›

Yes, x2 + 4x + 4, is a perfect square trinomial. Notice that the first and last terms of this trinomial are squared expressions.

What is an example of squaring a trinomial? ›

For example, suppose we wanted to square the trinomial x2 + 3x - 4. First, we'll identify the first term as a = x2, the second term as b = 3x, and the third term as c = -4. Now, we just plug the values into the formula and simplify! As we said earlier, it's just a matter of multiplying the terms and adding them up.

What is an example of a trinomial? ›

Examples of a trinomial expression: x + y + z is a trinomial in three variables x, y and z. 2a2 + 5a + 7 is a trinomial in one variables a. xy + x + 2y2 is a trinomial in two variables x and y.

### What is an example of a perfect square factoring? ›

When an expression has the general form a²+2ab+b², then we can factor it as (a+b)². For example, x²+10x+25 can be factored as (x+5)². This method is based on the pattern (a+b)²=a²+2ab+b², which can be verified by expanding the parentheses in (a+b)(a+b).

What is an example of a perfect square trinomial brainly? ›

Answer. Whenever you multiply a binomial by itself twice, the resulting trinomial is called a perfect square trinomial. For example, (x + 1) × (x + 1) = x2 + x + x + 1 = x2 + 2x + 1 and x2 + 2x + 1 is a perfect square trinomial.

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