Answer:
The expansion and simplified form is [tex]-4a^2+19a-12[/tex].
Further Explanation
One of the effective ways to expand when multiplying two binomial terms is by doing the FOIL Method. FOIL has the acronym F for First Terms, O for Outer Terms, I for Inner Terms, and L for Last terms.
Binomial terms/expression are terms that consist of two terms that make an expression.
1. [tex]2x+1[/tex]
2. [tex]a+b[/tex]
3. [tex](2a+b)^2[/tex]
1. The Binomial Theorem
2. The FOIL Method
Solution:
Do the FOIL method to do the expansion of the expression given. Multiply the first terms, outer terms, inner terms, and the last terms, then add all the products.
[tex](4a-3)(-a+4)[/tex]
F - First Terms [tex](4a)(-a)=-4a^2[/tex]
I - Inner Terms [tex](-3)(-a)=3a[/tex]
O - Outer Terms [tex](4a)(4)=16a[/tex]
L- Last Terms [tex](-3)(4)=-12[/tex]
Sum of All the Products:
[tex]\begin{aligned}-4a^2+3a+16a+(-12)=-4a^2+19a-12\end{aligned}[/tex]
The solution shows that the expansion and simplified form of [tex](4a-3)(-a+4)[/tex] is [tex]-4a^2+19a-12[/tex].
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