Find the product. -2x(x2 - 3) -2 x3 - 6 x -2 x2 6 x 6 x3 -2 x3 6 x.

1 answer:

6 0

Product of two polynomials can be done by distribution of multiplication over addition. The product of $-2x(x^2 - 3)$ is $-2x^3 + 6x$

<h3>What is distributive property of multiplication over addition?</h3>

Suppose a, b and c are three numbers. Then we have:

$a(b + c) = a\times b + a\times c$

(a(b+c) means a multiplied to (b+c). The sign of multiplication is usually hidden when using symbols and both quantities which are in multiplication are written together without space)

The product result of the given expression is

$-2x(x^2 - 3) = -2x^{1 + 2} + 6x = -2x^3 + 6x$

It is because when bases are same and there is multiplication, then powers add up, so we have: $a^b \times a^c = a^{b+c}$

Thus,

The product of $-2x(x^2 - 3)$ is $-2x^3 + 6x$

Learn more about product of polynomials here:

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50+51+52+...+101=...<br>Can you help me? I do not understand

Dmitriy789 [7]

Suppose

$S=50+51+52+\cdots+100+101$

At the same time, we can write

$S^*=101+100+99+\cdots+51+50$

Note that $S=S^*$ (just reverse the sum). Let's pair the first terms of $S$ and $S^*$ , and the second, and the third, and so on:

$S+S^*=(50+101)+(51+100)+(52+99)+\cdots+(100+51)+(101+50)$

Now, each grouped term in the sum on the right side adds to 151. There are 52 grouped terms on that same side (because there are 50 numbers in the range of integers 51-100, plus 50 and 101), which menas

$S+S^*=52\cdot151$