Question Video: Factorizing the Difference of Two Squares | Nagwa Question Video: Factorizing the Difference of Two Squares | Nagwa

# Question Video: Factorizing the Difference of Two Squares Mathematics • Second Year of Preparatory School

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Completely factor 9πβ΄ β 64πβ΄.

02:48

### Video Transcript

Completely factor nine π to the power of four minus 64π to the power of four.

And what we need to notice here is that nine is three squared, π to the power of four is π squared squared, 64 is eight squared, and π to the four is π squared squared. So we can think of this as three times three times π squared times π squared or, in fact, three π squared squared. Likewise, eight squared times π squared squared means eight times eight times π squared times π squared. And we can rearrange that, and itβs 18 squared all squared.

So we can rewrite the whole expression nine π to the power of four minus 64π to the power of four as three π squared all squared minus eight π squared all squared. And hopefully, youβll recognize this form as the difference of two squares. Itβs something all squared take away something else all squared. Now if you remember, the general format for this in terms of factoring it is π squared minus π squared, can be factored as π minus π times π plus π, and that makes sense if you think about it. Letβs multiply it out. π times π is π squared, positive π times positive π is positive ππ, negative π times positive π is negative ππ which we can rearrange as negative ππ, and negative π times positive π is negative π squared.

So weβve got π squared plus ππ minus ππ. So if we take- start off with ππ and take away ππ, weβve got nothing. So we can just cancel those two out like this. And then on the end, weβve got to take away π squared, or negative π squared. So this is just π squared minus π squared. So in our case, π squared is three π squared squared, so π is just three π squared. And π squared is eight π squared all squared, so π is just eight π squared.

So we can replace π and π, and our factored form becomes three π squared minus eight π squared times three π squared plus eight π squared. Although of course, you can write that the other way round. So you can put three π squared plus eight π squared first and three π squared minus eight π squared second.

So either one of those two is our completely factored form of nine π to the power of four minus 64π to the power of four.

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