College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Are you Ready for College Algebra? - B. Diagnostic Test: Algebraic Expressions - Page XVII: 1


a) $14x+7$ b) $x^{2}-2x-15$ c) $6x^{2}+x-2$ d) $a^{2}-4b^{2}$ e) $y^{2}-6y+9$ f) $4x^{2}+20x+25$

Work Step by Step

a) $14x+7$ $4(x+3)+5(2x-1)=4x+12+10x-5$ (Use the distributive property) $4x+12+10x-5=14x+7$ (Combine like terms) b) $x^{2}-2x-15$ $(x+3)(x-5)=x(x-5)+3(x-5)$ (Distribute the first parenthesis) $x(x-5)+3(x-5)=x^{2}-5x+3x-15$ (Distribute the x and 3) $x^{2}-5x+3x-15=x^{2}-2x-15$ (Combine like terms) c) $6x^{2}+x-2$ $(2x-1)(3x+2)=6x^{2}-3x+4x-2$ (Use FOIL, which is basically doing the same thing as in part b, but skipping a step) $6x^{2}-3x+4x-2=6x^{2}+x-2$ (Combine like terms) d) $a^{2}-4b^{2}$ $(a-2b)(a+2b)=a^{2}-(2b)^{2}$ (Using the difference of two squares formula) $a^{2}-(2b)^{2}=a^{2}-4b^{2}$ (Distributing the exponent) e) $y^{2}-6y+9$ $(y-3)^{2}=(y-3)(y-3)$ (Rewriting the expression) $(y-3)(y-3)=y^{2}-3y-3y+9$ (FOILing the expression) $y^{2}-3y-3y+9=y^{2}-6y+9$ (Combine like terms) f) $4x^{2}+20x+25$ $(2x+5)^{2}=(2x+5)(2x+5)$ (Rewriting the expression) $(2x+5)(2x+5)=4x^{2}+10x+10x+25$ (FOILing the expression) $4x^{2}+10x+10x+25=4x^{2}+20x+25$ (Combine like terms)
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