Subtracting an expression means adding its additive inverse, so change the sign of every term in (4x²y - 2xy). Note that yx² is identical to x²y by the commutative property of multiplication. Combining like terms yields 3xy - 3x²y.

Subtracting an expression means adding its additive inverse, so change the sign of every term in (4x²y - 2xy). Note that yx² is identical to x²y by the commutative property of multiplication. Combining like terms yields 3xy - 3x²y.

Quick Drill 1. Add the following terms. a) $3pq$ ; $-2pq$ ; $-5pq$ b) $-2m^2$ ; $-3mn$ ; $-3m^2$ c) $x^2y$ ; $-2xy^2$ ; $-3x^2y$ d) $a^2bc$ ; $-2ab^2c$ ; $-3a^2bc$ ; $-4ab^2c$ 2. Subtract $4x^2y - 2xy$ from $xy + yx^2$ . Practice 1 1. Add the following expressions. a) $x^2 + 2x + 1$ and $x^2 - 5x + 4$ b) $x - 2xy + y^2 + 7$ and $x^2 \dots$ c) $xz + yx + 3x - 20$ and $z - yx + xy + 12$ d) $xy + yz + zx + 5$ and $y\dots$ e) $2x^3 + 3x - 2$ , $x^2 - 3y + 4$ and $y^2 - xy + 2x$ f) $3y^4 - 2y^2 + 12$ , $y^3 - y\dots$

Answer: Quick Drill: 1(a) $-4pq$ , 1(b) $-5m^2 - 3mn$ , 1(c) $-2x^2y - 2xy^2$ , 1(d) $-2a^2bc - 6ab^2c$ ; 2. $3xy - 3x^2y$ . Practice 1: 1(a) $2x^2 - 3x + 5$ , 1(c) $xz + xy + 3x + z - 8$ , 1(e) $2x^3 + x^2 + 5x + y^2 - 3y - xy + 2$ . (Parts 1(b), 1(d), and 1(f) are truncated in the image).

Step-by-step solution

Step 1: Solve Quick Drill Question 1(a) and 1(b)

To add terms, combine like terms by adding their numerical coefficients. For (a), all three terms share the literal factor $pq$ , giving $(3 - 2 - 5)pq = -4pq$ . For (b), group the like terms $-2m^2$ and $-3m^2$ to obtain $-5m^2$ , leaving the unlike term $-3mn$ as it is.

Step 2: Solve Quick Drill Question 1(c) and 1(d)

In (c), identify like terms: $x^2y$ and $-3x^2y$ combine to $-2x^2y$ , while $-2xy^2$ is an unlike term because the exponents on $x$ and $y$ differ. In (d), group $a^2bc$ with $-3a^2bc$ to get $-2a^2bc$ , and group $-2ab^2c$ with $-4ab^2c$ to get $-6ab^2c$ .

Step 3: Solve Quick Drill Question 2

Subtracting an expression means adding its additive inverse, so change the sign of every term in $(4x^2y - 2xy)$ . Note that $yx^2$ is identical to $x^2y$ by the commutative property of multiplication. Combining like terms yields $3xy - 3x^2y$ .

Step 4: Solve Practice 1 Question 1(a)

Group like terms corresponding to $x^2$ , $x$ , and the constant terms together. Adding the coefficients gives $1 + 1 = 2$ for $x^2$ , $2 - 5 = -3$ for $x$ , and $1 + 4 = 5$ for the constants.

Step 5: Solve Practice 1 Question 1(c)

Since multiplication is commutative, $yx = xy$ . Thus, the terms $yx - yx + xy$ simplify to $xy$ . Combining the constants gives $-20 + 12 = -8$ , while the remaining terms $xz$ , $3x$ , and $z$ have no other like terms.

Step 6: Solve Practice 1 Question 1(e)

Collect like terms across the three expressions. The like linear terms in $x$ are $3x + 2x = 5x$ , and the constants are $-2 + 4 = 2$ . Arranging the remaining terms gives $2x^3 + x^2 + 5x + y^2 - 3y - xy + 2$ .

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