(4x4 – 3x3 – 18x2 + 15x – 3) (x2 – 5)

2 min read Jun 11, 2024
(4x4 – 3x3 – 18x2 + 15x – 3) (x2 – 5)

Expanding and Simplifying Algebraic Expressions

In this article, we will explore how to expand and simplify the algebraic expression (4x4 – 3x3 – 18x2 + 15x – 3)(x2 – 5).

Step 1: Expand the Expression

To expand the expression, we need to multiply each term in the first expression with each term in the second expression.

(4x4 – 3x3 – 18x2 + 15x – 3)(x2 – 5)

= (4x4)(x2) – (4x4)(5) – (3x3)(x2) + (3x3)(5) – (18x2)(x2) + (18x2)(5) + (15x)(x2) – (15x)(5) – 3(x2) + 3(5)

Step 2: Simplify the Expression

Now, let's simplify the expression by combining like terms.

= 4x6 – 20x4 – 3x5 + 15x3 – 18x4 + 90x2 + 15x3 – 75x – 3x2 + 15

= 4x6 – 20x4 – 3x5 + 30x3 – 18x4 – 3x2 + 75x + 15

In this simplified form, we can see that the expression has six terms, with the highest power of x being 6.

Conclusion

In conclusion, by expanding and simplifying the algebraic expression (4x4 – 3x3 – 18x2 + 15x – 3)(x2 – 5), we get a simplified expression with six terms, including a term with x6.

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