1957 AHSME Problems/Problem 4

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The first step in finding the product $(3x + 2)(x - 5)$ by use of the distributive property in the form $a(b + c) = ab + ac$ is:

$\textbf{(A)}\ 3x^2 - 13x - 10 \qquad  \textbf{(B)}\ 3x(x - 5) + 2(x - 5)\qquad \\ \textbf{(C)}\ (3x+2)x+(3x+2)(-5)\qquad \textbf{(D)}\ 3x^2-17x-10\qquad \textbf{(E)}\ 3x^2+2x-15x-10$

Solution

In order to find the product by using this form of the distributive property, we should express $(3x + 2)(x - 5)$ as $(3x + 2)(x) + (3x + 2)(-5)$. Thusly, $\boxed{\text{(C)}}$ is our answer, and we are done.

See also

1957 AHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 3
Followed by
Problem 5
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