What is the product of #2x^2 + 6x - 8# and #x + 3# in standard form?

1 Answer
Jim G.
Apr 10, 2016

# 2x^3 + 12x^2 + 10x - 24 #

Explanation:

The product of these expressions 'means' to multiply them.

hence : #color(blue)" (x + 3 )"(2x^2 + 6x - 8) #

Each term in the 2nd bracket must be multiplied by each term in the 1st.
This can be achieved as follows.

#color(blue)"x"(2x^2 + 6x - 8)color(blue)"+3"(x^2 + 6x - 8) #

# =[ 2x^3 + 6x^2 - 8x] + [6x^2 + 18x - 24 ]#

# =2 x^3 + 6x^2 - 8x +6x^2 + 18x - 24 #

collect 'like terms'

# =2 x^3 + 12x^2 + 10x - 24 " is in standard form "#

Writing an answer in standard form : Start with the term that has the highest power of the variable, in this case # x^3# , followed by terms with decreasing powers until the last term , usually a constant.

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