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17Calculus Precalculus - Factor Difference of Squares

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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.

Math Word Problems Demystified

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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Really UNDERSTAND Precalculus

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Practice Instructions

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

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