Answer :
To find the product of the polynomials [tex]\((5x^2 - 3)\)[/tex] and [tex]\((5x^2 - 3)\)[/tex], we need to use the distributive property. Here's a step-by-step explanation:
1. Write the expression: We start with [tex]\((5x^2 - 3)(5x^2 - 3)\)[/tex].
2. Apply the distributive property (also known as the FOIL method for two binomials):
- First, multiply the first terms: [tex]\(5x^2 \cdot 5x^2 = 25x^4\)[/tex].
- Outer, multiply the outer terms: [tex]\(5x^2 \cdot (-3) = -15x^2\)[/tex].
- Inner, multiply the inner terms: [tex]\((-3) \cdot 5x^2 = -15x^2\)[/tex].
- Last, multiply the last terms: [tex]\((-3) \cdot (-3) = 9\)[/tex].
3. Combine like terms:
- We have two middle terms, [tex]\(-15x^2\)[/tex] and [tex]\(-15x^2\)[/tex], which combine to [tex]\(-30x^2\)[/tex].
4. Write the final expanded and simplified polynomial:
- The expression becomes [tex]\(25x^4 - 30x^2 + 9\)[/tex].
Thus, the product of the polynomials [tex]\((5x^2 - 3)\)[/tex] and [tex]\((5x^2 - 3)\)[/tex] is [tex]\(\boxed{25x^4 - 30x^2 + 9}\)[/tex].
1. Write the expression: We start with [tex]\((5x^2 - 3)(5x^2 - 3)\)[/tex].
2. Apply the distributive property (also known as the FOIL method for two binomials):
- First, multiply the first terms: [tex]\(5x^2 \cdot 5x^2 = 25x^4\)[/tex].
- Outer, multiply the outer terms: [tex]\(5x^2 \cdot (-3) = -15x^2\)[/tex].
- Inner, multiply the inner terms: [tex]\((-3) \cdot 5x^2 = -15x^2\)[/tex].
- Last, multiply the last terms: [tex]\((-3) \cdot (-3) = 9\)[/tex].
3. Combine like terms:
- We have two middle terms, [tex]\(-15x^2\)[/tex] and [tex]\(-15x^2\)[/tex], which combine to [tex]\(-30x^2\)[/tex].
4. Write the final expanded and simplified polynomial:
- The expression becomes [tex]\(25x^4 - 30x^2 + 9\)[/tex].
Thus, the product of the polynomials [tex]\((5x^2 - 3)\)[/tex] and [tex]\((5x^2 - 3)\)[/tex] is [tex]\(\boxed{25x^4 - 30x^2 + 9}\)[/tex].
