Perfect Square Trinomial is the product of two binomials. But, both the binomials are same. When factoring some quadratics which gives identical factors, that quadratics are Perfect Square Trinomial.

The general forms of perfect square trinomial are

(ax - b)^{ 2} = (ax)^{2} - 2axb + b^{2}^{ }and (ax + b)^{ 2}= (ax)^{2 }+ 2axb + b^{2}

Related Calculators | |

Perfect Square Trinomial Calculator | Perfect Square Calculator |

Trinomial Calculator | Perfect Number Calculator |

A perfect square trinomial is one that factors into two identical factors. A trinomial of the form a^{2} + 2ab + b^{2} or a^{2 }- 2ab + b^{2} is a perfect square trinomial with factors (a + b)^{2} or (a - b)^{2} respectively.

The trinomial in the form ax^{2} + bx + c is perfect squre trinomial, if b^{2} = 4ac.

Below you can see the formulas for perfect square trinomials:

a^{2} + 2ab + b^{2} = (a + b)^{2}

a^{2} - 2ab + b^{2} = (a - b)^{2} ### Solved Example

**Question: **Factor using the perfect square trinomial formula x^{2} + 14x + 49.

** Solution: **

Perfect Square Trinomial is the product of two same binomials. In this, the first term and last term of the perfect square are perfect squares and the middle term is 2 times the square root of first terms times and square root of last terms.### Solved Examples

**Question 1: **Factor the trinomial x^{2} + 4x + 4

** Solution: **

**Question 2: **Factor the trinomial x^{2} + 8x + 16

** Solution: **

Given below are some of the examples on perfect square trinomials. ### Solved Examples

**Question 1: **Factor the trinomial x^{2} + 4x + 4

** Solution: **
**Question 2: **Factor the trinomial x^{2} + 8x + 16

** Solution: **
**Question 3: **Factor the trinomial x^{2} + 10x + 25

** Solution: **

The trinomial in the form ax

Below you can see the formulas for perfect square trinomials:

a

a

Given x^{2} + 14x + 49

The first and last terms are perfect squares.

=> x^{2} + 14x + 49 = **x**^{2} + 14x + **7**^{2}

The middle term is twice the product of the value x and the value 7.

=> 14x = 2 * 7x

Therefore, we can use the formula, a^{2} + 2ab + b^{2} = (a + b)^{2}

Thus, x^{2} + 14x + 49 = (x + 7)(x + 7) = (x + 7)^{2}

The first and last terms are perfect squares.

=> x

The middle term is twice the product of the value x and the value 7.

=> 14x = 2 * 7x

Therefore, we can use the formula, a

Thus, x

Perfect Square Trinomial is the product of two same binomials. In this, the first term and last term of the perfect square are perfect squares and the middle term is 2 times the square root of first terms times and square root of last terms.

Given x^{2} + 4x + 4

The above trinomial can be written as x^{2} + 2x + 2x + 4

Take x as common from first two terms,

x(x + 2) + 2x + 4

Take 2 as common from last two terms.

x(x + 2) + 2(x + 2)

(x + 2)(x + 2)

In this it is the product of two identical binomials

**(x + 2) ^{2 },** which is a perfect square.

Given x^{2} + 8x + 16

The above trinomial can be written as x^{2} + 4x + 4x + 16

Take x as common from first two terms,

x(x + 4) + 4x + 16

Take 4 as common from last two terms.

x(x + 4) + 4(x + 4)

(x + 4)(x + 4)

In this, it is the product of two identical binomials

**(x + 4) ^{2}**, which is a perfect square.

Given** **trinomial x^{2} + 4x + 4

In this, the first term is x^{2}, the second term is 2 times the square root of first term ($\sqrt{x^2}$ = x) and square root of second term ($\sqrt{4}$ = 2) and the third term 4 can be written as 2^{2} which is a perfect square.

In this, the first term is x

x^{2} + 4x + 4 = x^{2} + 2 * 2 * x + 4 = (x + 2)(x + 2) = (x + 2)^{2}.

This is the perfect square trinomial.

Given x^{2} + 8x + 16

In this, the first term is x^{2}, the second term is 2 times the square root of first term ($\sqrt{x^2}$ = x) and square root of second term ($\sqrt{16}$ = 4) and the third term 16 can be written as 4^{2} which is a perfect square.

In this, the first term is x

x^{2} + 8x + 16 = x^{2} + 2 * 4 * x + 4^{2} = (x + 4)(x + 4) = (x + 4)^{2}.

This is the perfect square trinomial.

Given x^{2} - 10x + 25

In this, the first term is x^{2}, the second term is -2 times the square root of first term ($\sqrt{x^2}$ = x) and square root of second term ($\sqrt{25}$ = 5) and the third term 25 can be written as 5^{2} which is a perfect square.

In this, the first term is x

x^{2} - 10x + 25 = x^{2} - 2 * 5 * x + 5^{2} = (x - 5)(x - 5) = (x - 5)^{2}.

This is the perfect square trinomial.

Related Topics | |

Math Help Online | Online Math Tutor |