Question

algebraic expressions
name:
equivalent expressions matching
date: period:
draw lines to match the algebra expression to its simplest form on the right.
$3(4n + 5)$ $-7n+ 20$
$4 - (n + 5)$ $-4n - 12$
$-4(2n + 3) + 4n$ $-12y + 8$
$(-5+ y)(-3)$ $3y+30$
$5(6 + y) - 2y$ $-n -1$
$-4(n-5)-3n$ $12n + 15$
$-2(6y - 4)$ $-2n - 7$
$5+4(2n-3)-10n$ $15 - 3y$

Explanation:

Step1: Simplify $3(4n + 5)$

Apply distributive property: $3\times4n + 3\times5 = 12n + 15$

Step2: Simplify $4 - (n + 5)$

Remove parentheses and combine terms: $4 - n - 5 = -n - 1$

Step3: Simplify $-4(2n + 3) + 4n$

Distribute then combine like terms: $-8n -12 + 4n = -4n -12$

Step4: Simplify $(-5 + y)(-3)$

Apply distributive property: $(-5)\times(-3) + y\times(-3) = 15 - 3y$

Step5: Simplify $5(6 + y) - 2y$

Distribute then combine like terms: $30 + 5y - 2y = 3y + 30$

Step6: Simplify $-4(n - 5) - 3n$

Distribute then combine like terms: $-4n + 20 - 3n = -7n + 20$

Step7: Simplify $-2(6y - 4)$

Apply distributive property: $-2\times6y + (-2)\times(-4) = -12y + 8$

Step8: Simplify $5 + 4(2n - 3) - 10n$

Distribute then combine terms: $5 + 8n -12 -10n = -2n -7$

Answer:

• $3(4n + 5) \longleftrightarrow 12N + 15$
• $4 - (n + 5) \longleftrightarrow -N -1$
• $-4(2n + 3) + 4n \longleftrightarrow -4N - 12$
• $(-5+ y)(-3) \longleftrightarrow 15 - 3Y$
• $5(6 + y) - 2y \longleftrightarrow 3Y+30$
• $-4(n-5)-3n \longleftrightarrow -7N+ 20$
• $-2(6y - 4) \longleftrightarrow -12Y + 8$
• $5+4(2n-3)-10n \longleftrightarrow -2N - 7$