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=

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

2.1.2 Area of LMPQ: This rectangle has length $8$ and width $x$. $Area = 8 \times x = 8x$ Area of LMPQ = $\boxed{8x}$

2.1.3 Area of RQTS: This rectangle has length $x$ and width $5$. $Area = x \times 5 = 5x$ Area of RQTS = $\boxed{5x}$

2.1.4 Area of QPTU: This rectangle has length $8$ and width $5$. $Area = 8 \times 5 = 40$ 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. $(x+8)(x+5) = Area of KLQR + Area of LMPQ + Area of RQTS + Area of QPTU$ $= x^2 + 8x + 5x + 40$ $= x^2 + 13x + 40$ The product is $\boxed{x^2 + 13x + 40}$.

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