Using your answers to 1.1 determine the area of ACEG in the simplest possible form: Area of ABJH Area of HJFG = Using your answer in 1.2 and 1.3 find the area of ACEG in the form ax2+bx+c=

Here are the solutions to the questions:

1.3 Using your answers to 1.1 determine the area of ACEG in the simplest possible form:
Area of ABJH $\underline{x^2}$ + Area of BCDJ $\underline{4x}$
Area of HJFG $\underline{3x}$ + Area of DEFJ $\underline{12}$
= $\boxed{x^2 + 7x + 12}$

1.4 Using your answer in 1.2 and 1.3 find the area of ACEG in the form $ax^2 + bx + c = \boxed{x^2 + 7x + 12}$

1.5 To find the product of $(x+6)(x+4)$, we multiply each term in the first binomial by each term in the second binomial.

$$(x+6)(x+4) = x \cdot x + x \cdot 4 + 6 \cdot x + 6 \cdot 4$$ $$= x^2 + 4x + 6x + 24$$ $$= x^2 + 10x + 24$$

The product is $\boxed{x^2 + 10x + 24}$.

QUESTION 2

2.1 Use the method you discovered in question 1 to determine the product of $(x+8)(x+5)$.
The large rectangle KSMU has a total length of $(x+8)$ and a total width of $(x+5)$.

2.1.1 Area of KLQR:
This rectangle has length $x$ and width $x$.

$$\text{Area} = x \times x = x^2$$

Area of KLQR = $\boxed{x^2}$

2.1.2 Area of LMPQ:
This rectangle has length 8 and width $x$.

$$\text{Area} = 8 \times x = 8x$$

Area of LMPQ = $\boxed{8x}$

2.1.3 Area of RQTS:
This rectangle has length $x$ and width 5.

$$\text{Area} = x \times 5 = 5x$$

Area of RQTS = $\boxed{5x}$

2.1.4 Area of QPTU:
This rectangle has length 8 and width 5.

$$\text{Area} = 8 \times 5 = 40$$

Area of QPTU = $\boxed{40}$

2.1.5 $(x+8)(x+5)$:
The product is the sum of the areas of the four smaller rectangles.

$$(x+8)(x+5) = \text{Area of KLQR} + \text{Area of LMPQ} + \text{Area of RQTS} + \text{Area of QPTU}$$ $$= x^2 + 8x + 5x + 40$$ $$= x^2 + 13x + 40$$

The product is $\boxed{x^2 + 13x + 40}$.