## 17Calculus Precalculus - Factor Difference of Squares

##### 17Calculus

Factoring Difference of Two Squares

A special case that you will definitely come across in calculus is the difference of two squares.
The difference of two squares equation is pretty easy.

$$a^2 - b^2 = (a+b)(a-b)$$

Note - There is no equation to factor the sum to two squared terms, i.e. $$a^2 + b^2$$ where you end up with real terms. Since calculus uses mostly real numbers, you won't need to factor the sum of two squares until you start working with complex numbers.
Okay, let's use the formula for the difference of two squares on some practice problems.

### Practice

Unless otherwise instructed, factor these polynomials, giving your answers in exact form.

$$x^4 - 81$$

Problem Statement

Unless otherwise instructed, factor the polynomial $$x^4 - 81$$

Solution

### Freshmen Math Doctor - 2547 video solution

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$$36x^2 - 49y^2$$

Problem Statement

Unless otherwise instructed, factor the polynomial $$36x^2 - 49y^2$$

Solution

### Freshmen Math Doctor - 2548 video solution

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$$64x^2 - 81$$

Problem Statement

Unless otherwise instructed, factor the polynomial $$64x^2 - 81$$

Solution

### Freshmen Math Doctor - 2549 video solution

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$$x^2 - 144$$

Problem Statement

Unless otherwise instructed, factor the polynomial $$x^2 - 144$$

Solution

### Freshmen Math Doctor - 2550 video solution

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$$16x^2 - 81y^4$$

Problem Statement

Unless otherwise instructed, factor the polynomial $$16x^2 - 81y^4$$

Solution

### 2645 video solution

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$$9x^2 - 49$$

Problem Statement

Unless otherwise instructed, factor the polynomial $$9x^2 - 49$$

Solution

### 2646 video solution

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$$36y^4 - 100$$

Problem Statement

Unless otherwise instructed, factor the polynomial $$36y^4 - 100$$

Solution

### 2647 video solution

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$$16x^2 - 25y^2$$

Problem Statement

Unless otherwise instructed, factor the polynomial $$16x^2 - 25y^2$$

Solution

### 2648 video solution

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$$64x^2 - 81y^2$$

Problem Statement

Unless otherwise instructed, factor the polynomial $$64x^2 - 81y^2$$

Solution

### 2649 video solution

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$$(x-3)^2 - 4$$

Problem Statement

Unless otherwise instructed, factor the polynomial $$(x-3)^2 - 4$$

Solution

### 2650 video solution

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$$(x+7)^2 - 25$$

Problem Statement

Unless otherwise instructed, factor the polynomial $$(x+7)^2 - 25$$

Solution

### 2651 video solution

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$$(x+2)^2 - 25$$

Problem Statement

Unless otherwise instructed, factor the polynomial $$(x+2)^2 - 25$$

Solution

### 2652 video solution

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