To simplify the expression (5x - 3x^2) (5x - 2) • (10x + 7x^2) and write it in standard form, we can start by expanding the expression using the distributive property. Let's break it down step by step:
(5x - 3x^2) (5x - 2) • (10x + 7x^2)
Expanding the first two terms:
= (25x^2 - 10x - 15x^3 + 6x^2) • (10x + 7x^2)
Now, let's distribute the terms in the first expression with each term in the second expression:
= 25x^2 • 10x + 25x^2 • 7x^2 - 10x • 10x - 10x • 7x^2
15x^3 • 10x - 15x^3 • 7x^2 + 6x^2 • 10x + 6x^2 • 7x^2
Simplifying each term:
= 250x^3 + 175x^4 - 100x^2 - 70x^4 - 150x^4 - 105x^5 + 60x^3 + 42x^4
Combining like terms:
= -105x^5 + 175x^4 - 70x^4 - 150x^4 + 42x^4 + 250x^3 + 60x^3 - 100x^2
Finally, arranging the terms in descending order of exponents:
= -105x^5 + (175 - 70 - 150 + 42)x^4 + (250 + 60)x^3 - 100x^2
Simplifying further:
= -105x^5 - 253x^4 + 310x^3 - 100x^2
Therefore, the equivalent expression in standard form is:
-105x^5 - 253x^4 + 310x^3 - 100x^2