4.1 Algebraic expressions

What does the coefficient of a quantity tell us?

The difference between coefficients and exponents

Coefficients record the number of like terms in an algebraic expression.
$\begin{array}{cc}\underset{4\text{terms}}{\underbrace{x+x+x+x}}=& \underset{\text{coefficient}\text{is}4}{\underset{}{4x}}\end{array}$
Exponents record the number of like factors in a term.
$\begin{array}{cc}\underset{4\text{factors}}{\underbrace{x\cdot x\cdot x\cdot x}}=& \underset{\text{exponent}\text{is}4}{\underset{}{x^4}}\end{array}$

In a term, the coefficient of a particular group of factors is the remaining group of factors.

Determine the coefficients.
In the term $6x^3$ , the coefficient of
(a) $x^3$ is .
(b) 6 is .

In the term $3x(y-1)$ , the coefficient of
(a) $x(y-1)$ is .
(b) $(y-1)$ is .
(c) $3(y-1)$ is .
(d) $x$ is .
(e) 3 is .
(f) The numerical coefficient is .

In the term $10a{b}^4$ , the coefficient of
(a) $a{b}^4$ is .
(b) $b^4$ is .
(c) $a$ is .
(d) 10 is .
(e) $10a{b}^3$ is .

What is an algebraic expression?

Why is the number 14 considered to be an expression?

Why is the number $x$ considered to be an expression?

$2x+1$

$6x-10$

$2x^3+x-15$

$5x^2+6x-2$

$3x$

$5cz$

2

61

$x$

$4y^3$

$17a{b}^2$

$a+1$

$(a+1)$

$2x+x+7$

$2x+(x+7)$

$(a+1)+(a-1)$

$a+1+(a-1)$

$x^2+5x^2-2x^2$

$11y^3-33y^3$

$45a{b}^2+9b^2$

$6x^2{y}^3+18x^2$

$2(a+b)-3(a+b)$

$8a^2(b+1)-10a^2(b+1)$

$14a{b}^2{c}^2(c+8)+12a{b}^2{c}^2$

$4x^{2}y+5a^{2}b$

$9a{(a-3)}^2+10b(a-3)$

$15x^2-30x{y}^2$

$12a^3{b}^{2}c-7(b+1)(c-a)$

$0.06a{b}^2+0.03a$

$5.2{(a+7)}^2+17.1(a+7)$

$\frac{3}{4}{x}^2{y}^2{z}^2+\frac{3}{8}{x}^2{z}^2$

$\frac{9}{16}(a^2-b^2)+\frac{9}{32}(b^2-a^2)$

$a\text{'}\text{s}\text{in}4a?$

$z\text{'}\text{s}\text{in}12z?$

$x^2\text{'s}\text{in}5x^2?$

$y^3\text{'s}\text{in}6y^3?$

$xy\text{'}\text{s}\text{in}9xy?$

$a^{2}b\text{'}\text{s}\text{in}10a^{2}b?$

$(a+1)\text{'}\text{s}\text{in}4(a+1)?$

$(9+y)\text{'}\text{s}\text{in}8(9+y)?$

${\text{y}}^2\text{'s}\text{in}3x^3{y}^2\text{?}$

$12x\text{'}\text{s}\text{in}12x^2{y}^5?$

$(a+5)\text{'}\text{s}\text{in}2(a+5)?$

$(x-y)\text{'}\text{s}\text{in}5x(x-y)?$

$(x+1)\text{'}\text{s}\text{in}8(x+1)?$

$2\text{'}\text{s}\text{in}2x^2(x-7)?$

$3(a+8)\text{'}\text{s}\text{in}6x^2{(a+8)}^3(a-8)?$

$7y;y$

$10x;x$

$5a;5$

$12a^2{b}^3{c}^2{r}^7;a^2{c}^2{r}^7$

$6x^2{b}^2(c-1);c-1$

$10x{(x+7)}^2;10(x+7)$

$9a^2{b}^5;3a{b}^3$

$15x^4{y}^4{\left(z+9a\right)}^3;\left(z+9a\right)$

$\left(-4\right)a^6{b}^2;ab$

$\left(-11a\right){\left(a+8\right)}^3\left(a-1\right);{\left(a+8\right)}^2$

( [link] ) Simplify ${\left[\frac{2x^8{\left(x-1\right)}^5}{x^4{\left(x-1\right)}^2}\right]}^4$ .

( [link] ) Supply the missing phrase. Absolute value speaks to the question of and not "which way."

( [link] ) Find the value of $-\left[-6(-4-2)+7(-3+5)\right]$ .

( [link] ) Find the value of $\frac{2^5-4^2}{3^{-2}}$ .

( [link] ) Express $0.0000152$ using scientific notation.