Multiplying Binomials

Name

Class

Date

8-3

Enrichment

You can find the volume of irregular figures by dividing the figure into smaller rectangular prisms, finding the volume of each separate figure, and then adding them together. The figure to the right can be divided into two rectangular prisms.

V1 = (x + 1)(x + 1)(x – 1)

= (x 2 + 2x + 1)(x – 1)

= x3+ x2 – x –1

Subtract to find the length of Prism 2. (2x + 3) – (x + 1) = x + 2

V2 = (x + 2)(x – 1)(2x – 2)

= (x2 + x – 2)(2x – 2)

= 2x3 – 6x + 4

VTotal= (x3+ x2 – x – 1) + (2x3 – 6x + 4)

= 3x3+ x2 – 7x + 3

You can also find the volume of an irregular figure by finding the volume of the whole figure, as if no pieces were cut away. Next, find the volume of the cut away piece, and then subtract that volume from the whole. Prism 2 is x – 3 taller than Prism 1.

VWhole= (x – 1)(2x + 3)(2x – 2) = (2x2 + x – 3)(2x – 2) = 4x3 – 2x2 – 8x + 6

VPiece= (x – 1)(x + 1)(x – 3) = (x2 – 1)(x – 3) = x3 – 3x2 – x + 3

VTotal= (4x3 – 2x2 – 8x + 6) – (x3 – 3x2 – x + 3) = 3x3+ x2 – 7x + 3

What is the volume of each figure? Write your answer as a polynomial in standard form.

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Prentice Hall Algebra 1 •Teaching Resources