Question

error alerti
some addition and subtraction problems look very similar to distributive property
problems.
ex. -3(x + 7) this expression requires the distributive property.
(5 - x)(-2) this expression requires the distributive property.
(5 - x) - 8 and 2(n • 4) these expressions do not!

1. circle the problems that require the distributive property. put an x through

those that do not require the distributive property.
-a(3 + b) (-a)(3) + (b) (3 + b) - a (3 + b)(-a)
4(2 • n) (3 - g)(-5) (-4)(6) + n (8 + h) - 2
should i use the distributive property??

Explanation:

Step1: Recall the distributive property formula

The distributive property is \(a(b + c)=ab+ac\). We need to check if each expression can be written in this form.

Step2: Analyze each expression

• For \(-a(3 + b)\): Using the distributive property \(a=-a\), \(b = 3\), \(c=b\), we get \(-a\times3+(-a)\times b=-3a - ab\). So it requires the distributive property.
• For \((-a)(3)+(b)\): This is just a sum of two terms \(-3a + b\), no distribution over a sum or difference inside parentheses. So it does not require the distributive property.
• For \((3 + b)-a\): This is a subtraction of \(a\) from the sum \((3 + b)\), no multiplication over a sum. So it does not require the distributive property.
• For \((3 + b)(-a)\): Using the distributive property \(a=-a\), \(b = 3\), \(c=b\), we get \((-a)\times3+(-a)\times b=-3a - ab\). So it requires the distributive property.
• For \(4(2\cdot n)\): This is \(4\times2n = 8n\), just multiplication of constants and a variable, no distribution over a sum. So it does not require the distributive property.
• For \((3 - g)(-5)\): Using the distributive property \(a=-5\), \(b = 3\), \(c=-g\), we get \((-5)\times3+(-5)\times(-g)=-15 + 5g\). So it requires the distributive property.
• For \((-4)(6)+n\): This is a sum of \(-24\) and \(n\), no multiplication over a sum. So it does not require the distributive property.
• For \((8 + h)-2\): This is a subtraction of \(2\) from the sum \((8 + h)\), no multiplication over a sum. So it does not require the distributive property.

Answer:

Expressions that require the distributive property: \(-a(3 + b)\), \((3 + b)(-a)\), \((3 - g)(-5)\)
Expressions that do not require the distributive property: \((-a)(3)+(b)\), \((3 + b)-a\), \(4(2\cdot n)\), \((-4)(6)+n\), \((8 + h)-2\)