Question

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lesson: 5.2 (day 1)
1 write (5x + 3)(x² - 8x + 2) in standard form.
2 multiply (-2ab + 4a)(5b² - 4b + a).

Explanation:

Step1: Distribute 5x to trinomial

$5x(x^2 - 8x + 2) = 5x^3 - 40x^2 + 10x$

Step2: Distribute 3 to trinomial

$3(x^2 - 8x + 2) = 3x^2 - 24x + 6$

Step3: Combine like terms

$5x^3 - 40x^2 + 10x + 3x^2 - 24x + 6 = 5x^3 - 37x^2 - 14x + 6$

Step4: Distribute $-2ab$ to trinomial

$-2ab(5b^2 - 4b + a) = -10ab^3 + 8ab^2 - 2a^2b$

Step5: Distribute $4a$ to trinomial

$4a(5b^2 - 4b + a) = 20ab^2 - 16ab + 4a^2$

Step6: Combine like terms

$-10ab^3 + 8ab^2 - 2a^2b + 20ab^2 - 16ab + 4a^2 = -10ab^3 + 28ab^2 - 2a^2b - 16ab + 4a^2$

Answer:

1. $5x^3 - 37x^2 - 14x + 6$
2. $-10ab^3 + 28ab^2 - 2a^2b - 16ab + 4a^2$