To find the value of [tex]\(5432 \times (-34) + (-5432) \times 66\)[/tex], we can utilize the distributive property of multiplication over addition.
The distributive property states that [tex]\(a(b + c) = ab + ac\)[/tex]. In this context, the expression can be transformed to help simplify the computation:
Given the expression:
[tex]\[5432 \times (-34) + (-5432) \times 66,\][/tex]
we can see a common factor between the terms, which is [tex]\(5432\)[/tex].
Let us rewrite the expression as:
[tex]\[5432 \times (-34) + (-5432) \times 66 = 5432 \times (-34) + 5432 \times (-66).\][/tex]
Notice that [tex]\((-5432) \times 66\)[/tex] can be expressed as [tex]\((5432) \times (-66)\)[/tex] because multiplying by a negative number changes the sign of the product.
Now, combine the common factor [tex]\(5432\)[/tex]:
[tex]\[5432 \times [-34 + (-66)].\][/tex]
Now simplify inside the brackets:
[tex]\[-34 + (-66) = -34 - 66 = -100.\][/tex]
So the expression is now:
[tex]\[5432 \times (-100).\][/tex]
We can now perform the multiplication:
[tex]\[5432 \times (-100) = -543200.\][/tex]
Hence, the value of the expression [tex]\(5432 \times (-34) + (-5432) \times 66\)[/tex] is:
[tex]\[\boxed{-543200}.\][/tex]
