Question

1. 4x(2x² + y)

8x³ + 4xy
7(a) x²(2x + 9)
2x³ + 9x²

1. (2x - 3)(3x - 5)

6x² - 10x - 9x + 15
6x² - 19x + 15

1. (a + b)(a² - 3ab - b²)

a(-b²) =

Explanation:

Step1: Verify 24) distribution

$4x(2x^2 + 5) = 4x \cdot 2x^2 + 4x \cdot 5 = 8x^3 + 20x$

Step2: Verify 26) distribution

$x^2(2x + 9) = x^2 \cdot 2x + x^2 \cdot 9 = 2x^3 + 9x^2$

Step3: Correct 28) FOIL calculation

$(2x-3)(3x-5) = 2x\cdot3x + 2x\cdot(-5) + (-3)\cdot3x + (-3)\cdot(-5) = 6x^2 -10x -9x +15$
Combine like terms: $6x^2 -19x +15$

Step4: Expand 20) via distribution

$(a+b)(a^2 -3ab -b^2) = a(a^2 -3ab -b^2) + b(a^2 -3ab -b^2)$
$= a^3 -3a^2b -ab^2 + a^2b -3ab^2 -b^3$
Combine like terms: $a^3 -2a^2b -4ab^2 -b^3$

Answer:

1. 24) Corrected: $8x^3 + 20x$ (original had $4x5$ instead of $20x$)
2. 26) Correct: $2x^3 + 9x^2$
3. 28) Corrected: $6x^2 -19x +15$ (original had sign/arithmetic errors)
4. 20) Expanded: $a^3 -2a^2b -4ab^2 -b^3$