QuestionMultiply the polynomials: $(5 x^{2}+y)(x^{2}-3 y)$ .

Studdy Solution

STEP 1

Assumptions1. We are multiplying two binomial expressions $(5x^+y)$ and $(x^-3y)$ . . We will use the distributive property of multiplication over addition to multiply these binomials.

STEP 2

First, we distribute the first term of the first binomial $(5x^2)$ to each term in the second binomial $(x^2-y)$ .
$5x^2 \cdot (x^2 -y)$

STEP 3

Perform the multiplication for each term.
$5x^2 \cdot x^2 -5x^2 \cdot3y$

STEP 4

implify the multiplication.
$x^4 -15x^2y$

STEP 5

Next, we distribute the second term of the first binomial $(y)$ to each term in the second binomial $(x^2-3y)$ .
$y \cdot (x^2 -3y)$

STEP 6

Perform the multiplication for each term.
$y \cdot x^2 - y \cdot3y$

STEP 7

implify the multiplication.
$yx^2 -3y^2$

STEP 8

Combine the results from4 and7 to get the final result.
$5x^4 -15x^2y + yx^2 -3y^2$ The multiplication of the given polynomials is $5x^4 -15x^2y + yx^2 -3y^2$ .

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