91Ó°ÊÓ

$$\begin{gathered} Giveninformation: \\ \left(a\right){(6x+7)}^2\left(b\right)(3x-4)(3x+4) \\ \left(c\right)(2x-5)(5x-2) \\ \left(d\right){(6n-1)}^2 \end{gathered}$$

Conjugate Pair

Aconjugate pair is two binomials of the form

(²¹âˆ’b),(²¹+²ú).(²¹âˆ’b),(²¹+²ú).

The pair of binomials each have the same first term and the same last term, but one binomial is a sum and the other is a difference.

We are asked to square a binomial.it fits the binomial squares pattern.

$$\begin{gathered} {(6x+7)}^2 \\ Usethepattern6x^2+2.6x.7+{\left(7\right)}^2 \\ Simplify6x^2+84x+49 \end{gathered}$$

$$\begin{gathered} \left(b\right) \\ Theseareconjugates.Theyhavethesamefirstnumbersandsamelastnumbers,andonebinomialisasumandotherisadifference. \\ Itfitstheproductofconjugatepatterns. \\ (3x-4)(3x+4) \\ UsethePattern{\left(3x\right)}^2-{\left(4\right)}^2 \\ Simplify3x^2-16 \end{gathered}$$

$$\begin{gathered} \left(c\right)(2x-5)(5x-2) \\ Thisproductdoesnotfitthepatterns,sowewillusetheFOIL. \\ UseFOIL10x^2-4x-25x+10 \\ Simplify10x^2-29x+10 \end{gathered}$$

$$\begin{gathered} \left(d\right){(6n-1)}^2 \\ Again,wewillsquareabinomialsoweusethebinomialsquarespattern \\ Usethepattern{\left(6n\right)}^2-2.6n.1+1^2 \\ Simplify6n^2-12n+1 \end{gathered}$$