Use the distributive property to expand the linear expression.
3(4x + 3)
Starting with the expression 3(4x + 3), we can distribute the 3 to both terms inside the parentheses.
3 * 4x + 3 * 3
This simplifies to:
12x + 9
So, the expanded form of the expression 3(4x + 3) is 12x + 9.
Steven will factor the expression 42xyz + 56xy – 7x by dividing each term by a common factor. Which possible common factor could Steven use? (choose 2)
Responses
A 77
B yy
C zz
D xx
E 6
To find a common factor to divide each term by, we need to look for factors that are present in all terms of the expression.
Looking at the terms 42xyz, 56xy, and 7x, we see that the common factors among all of them are 7 and x.
Therefore, the possible common factors that Steven could use are:
A) 77: This is not a common factor of all terms.
B) yy: This is not a common factor of all terms.
C) zz: This is not a common factor of all terms.
D) xx: This is a common factor of all terms, as all terms contain x.
E) 6: This is not a common factor of all terms.
The possible common factors that Steven could use are D) xx.
Steven will factor the expression 42xyz + 56xy – 7x by dividing each term by a common factor. Which possible common factor could Steven use? (choose 2)
Responses
A 7
B y
C z
D x
E 6
To find the common factor that can be used to divide each term of the expression, we need to identify the factors that are present in every term.
In the given expression 42xyz + 56xy - 7x, the common factors among all terms are 7 and x.
Therefore, the possible common factors that Steven could use are:
A) 7: This is a common factor, as all terms contain a factor of 7.
B) y: This is not a common factor of all terms.
C) z: This is not a common factor of all terms.
D) x: This is a common factor of all terms, as all terms contain a factor of x.
E) 6: This is not a common factor of all terms.
The possible common factors that Steven could use are A) 7 and D) x.
To expand the linear expression 3(4x + 3) using the distributive property, you need to distribute the 3 to both terms inside the parentheses.
First term: 3 * 4x = 12x
Second term: 3 * 3 = 9
Therefore, the expanded expression using the distributive property is 12x + 9.
To expand the linear expression 3(4x + 3) using the distributive property, we need to multiply each term inside the parentheses by the number outside the parentheses.
First, let's distribute the 3 to the terms inside the parentheses:
3 * 4x = 12x (multiply 3 by 4x)
3 * 3 = 9 (multiply 3 by 3)
Now we can rewrite the expression with the expanded form:
3(4x + 3) = 12x + 9
Therefore, the expanded form of the linear expression 3(4x + 3) is 12x + 9.