Examples with solutions for Variables and Algebraic Expressions: Comparison to an existing expression

Exercise #1

Which expressions are equal to the following:

9a+5n 9a+5n

a. 4(a+n)+5an 4(a+n)+5a\cdot n

b. 3(an)+6a+8n 3(a-n)+6a+8n

c. 20a7n11a+12n 20a-7n-11a+12n

d. 10an+6an 10a-n+6a-n

e. 9(a+n)4n2 9(a+n)-\frac{4n}{2}

f. 3(a+n)(n5)+24a3n23an+20n 3(a+n)(n-5)+24a-3n^2-3an+20n

Video Solution

Answer

b, c, f

Exercise #2

Which of the following expressions are equivalent to the following:

9y+4x+35 9y+4x+35

a. 3y+2x+6y+30+7 3y+2x+6y+30+7

b. 5y+3x+4y+30+x+5 5y+3x+4y+30+x+5

c. 4x+30+9y+5 4x+30+9y+5

d. 3(3y+10)+5+22x 3(3y+10)+5+2\cdot2x

e. 5(8+x)x+3y3y5 5(8+x)-x+3y\cdot3y-5

f. 2x2+3(2y+10)+5+3y 2x\cdot2+3(2y+10)+5+3y

Video Solution

Answer

b. c. d. f.

Exercise #3

Which expressions represent the same value?

45+5a+3ab+27b 45+5a+3ab+27b

a. (5+3b)(a+9) (5+3b)(a+9)

b. 45+23a+413ab+(3a+27)b 45+\frac{2}{3}a+4\frac{1}{3}ab+(3a+27)b

c. 2ab+5(9+a)+ab+9a3ba1 2ab+5(9+a)+ab+\frac{9}{a}\cdot\frac{3ba}{1}

d. 45+8ab+27b 45+8ab+27b

Video Solution

Answer

a. c. d. (d. depends on b)

Exercise #4

Which expressions are equal to the following: 79x+34y2 \frac{7}{9}x+\frac{3}{4}y^2

a. 34y(y+x)+x36 \frac{3}{4}y(y+x)+\frac{x}{36}

b. 4772x+18xy2+58y2 \frac{47}{72}x+\frac{1}{8}xy^2+\frac{5}{8}y^2

c. 79(x+y)45y2 \frac{7}{9}(x+y)-\frac{4}{5}y^2

d. 29x+59y2+79xy+14y2 \frac{2}{9}x+\frac{5}{9}y^2+\frac{7}{9}xy+\frac{1}{4}y^2

e. (x+y)(19+34y)+23x34xy+19y (x+y)(\frac{1}{9}+\frac{3}{4}y)+\frac{2}{3}x-\frac{3}{4}xy+\frac{1}{9}y

f. 97y2+43x \frac{9}{7}y^2+\frac{4}{3}x

Video Solution

Answer

e