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5-89.

Find the missing areas and dimensions for each generic rectangle below. Then write each area as a sum and as a product.

Generic rectangle left edge top $4x$
interior top left $16x^2$
interior top right blank
left edge bottom blank
interior bottom left blank
interior bottom right $1$

Answer (a):
$\left(4x + 1\right)\left(4x + 1\right) = 16x^{2} + 8x +1$

Generic rectangle interior top left $10y$
interior top right blank
interior bottom left blank
interior bottom right $-12x$
bottom edge left $2y$
bottom edge right $-3$

Hint 1(b):
What must be multiplied by $2y$ to get $10y$ ? Put that expression where the blue circle is.

Generic rectangle left edge top blue circle $\ \enclose{circle}[mathcolor="blue"]{{ \ }}$

interior top left $10y$

interior top right blank

left edge bottom

interior bottom left blank

interior bottom right $-12x$

bottom edge left $2y$

bottom edge right $-3$

Hint 2(b):
What must be multiplied by $−3$ to get $−12x$ ? Put that expression where the blue circle is.

Generic rectangle left edge top blank

interior top left $10y$

interior top right blank

left edge bottom blue circle $\ \enclose{circle}[mathcolor="blue"]{{ \ }}$

interior bottom left blank

interior bottom right $-12x$

bottom edge left $2y$

bottom edge right $-3$

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