Question

multiply.
$(2x^{2} + 4x - 3)(x^{2} - 2x + 5)$
$2x^{4} + 7x^{2} - 15$
$2x^{4} - 8x^{2} - 15$
$2x^{4} - x^{2} + 26x - 15$
$2x^{4} + 8x^{3} - x^{2} + 26x - 15$
done

Explanation:

Step1: Distribute first polynomial terms

$2x^2(x^2 - 2x + 5) + 4x(x^2 - 2x + 5) - 3(x^2 - 2x + 5)$

Step2: Expand each product

$2x^4 - 4x^3 + 10x^2 + 4x^3 - 8x^2 + 20x - 3x^2 + 6x - 15$

Step3: Combine like terms

$2x^4 + (-4x^3 + 4x^3) + (10x^2 - 8x^2 - 3x^2) + (20x + 6x) - 15$

Step4: Simplify each term group

$2x^4 + 0x^3 - x^2 + 26x - 15$

Answer:

$2x^4 - x^2 + 26x - 15$ (Option 3: $2x^4 - x^2 + 26x - 15$)