Question

Find the product of 2x4(3x2 4x 1). 6x6 8x5 2x4 6x8 8x4 1 5x6 6x5 3x4 5x8 6x4 1.

Answer 1

Product of polynomials can be done by using distributive property of multiplication over addition. The needed product is: Option

What is distributive property of multiplication over addition?

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)

What are like terms?

Those terms which have same variables raised with same powers.

For example, $5x^3$ and $x^3$ are like terms since variable is same, and it is raised to same power 3.

For example $x^3$ and $4x^4$ are not like terms as the variables are same but powers aren't same.

For the given case, the expression is $2x^4(3x^2 +4x +1)$

Using the distributive property of multiplication over addition, we get the product result as:

$2x^4(3x^2 +4x +1) = 6x^{4+2} + 8x^{4+1} + 2x^4 = 6x^6 + 8x^5 + 2x^4$

(when like terms are multiplied, powers are added of the variables (same variable) due to property  $a^b \times a^c = a^{b+c}$ )

Learn more about product of polynomials here:

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