-(x2-%E2%80%93-5).jpeg "(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.
