Question

find the missing term.

1. $(4x + 3)(9x^2 + 7x - 3)=36x^3 + 55x^2 + ? - 9$

$? = $

1. $(2x^2 + 7x - 6)(5x + 9)=? + 53x^2 + 33x - 54$

$? = $
find the area of the shape.

Explanation:

Step1: Expand first product (x term)

Calculate terms giving $x$: $4x(-3) + 3(7x) = -12x + 21x$

Step2: Simplify for first missing term

$-12x + 21x = 9x$

Step3: Expand second product (x³ term)

Calculate term giving $x^3$: $2x^2(5x) = 10x^3$

Step4: Calculate triangle area formula

Area = $\frac{1}{2} \times \text{base} \times \text{height}$

Step5: Substitute base and height

$\frac{1}{2}(3x^2 + 5x - 6)(2x^3)$

Step6: Distribute to simplify

$(3x^2 + 5x - 6)x^3 = 3x^5 + 5x^4 - 6x^3$

Answer:

1. $9x$
2. $10x^3$
3. $3x^5 + 5x^4 - 6x^3$