7th Grade Math
Name:_______ Class: _________
13.4-13.5 Quiz
Is the expression a monomial?
a. 7 x 2 y ______
b. 7 2 xy ______
e. 8 x 2 a ______
f.
i. 2 x y ______
ab
______
7
j. 0.3x2y ______
c. 8 2 xa ______
g.
d.
7
______
ab
6ab 2 ______ h. 6 ab 2 ______
State whether the polynomial is a monomial, a binomial, a trinomial or none of
these.
a. 2 x  3 y  4 z ______ b. 2 x  11 _____ c.  +ab ___
d. x 4  4 x  4 ______
5
e. 3a 2  6a 1  4 ______ f. 3a 2  6a  4 1 _____g. 2 x 3 
h.  2 xyzt ______
3y
y3
i. 6 x 2  2 x 1  6 ______ j. 4 x 3 
______
k.  4a 3  2 x ______
3
Simplify each expression.
2
2
2
2
2
2
2
2
22. (4 xy  2 x  4 y )  (3x  6 xy  8 y ) 23) (4 xy  2 x  4 y )  (3x  6 xy  8 y )
2
2
2
2
2
2
2
2
2  (4 xy  2 x  4 y )  (3x  6 xy  8 y ) 25)  (4 xy  2 x  4 y )  (3x  6 xy  8 y )
(4xy2x2+3y2)+(x25xy7y2)
26)
(2x2+4x5)+(8x+5x2+6)
27)
28)
(7x25xy6y)(3xy+5x211y)
29) (5x27xy12y2)(5xy+36y2)
30)
(2x24x+1)(2x24x1)
31)
3
5
(2 x 2  3 x  1)  (4  3 x  x 2 )
2
2
32)
1 2
 1

ab   3a 2b  ab2     ba 2  2a    5a  3
2
 4

33)  8ab  7b    6b  9ab 
13.6 Multiplying polynomial by a monomial
I. Distributing a monomial
Example 1: -4y2(5y4-3y2+2)=
Exercise 1 : simplify each product
a. 4b(ab2+b+6)
b. -7h(3h2-8h-1)
c. 2x(x2-6x+5)
d. -3a(4a2-5a+9)
f. y(y+3)-5y(y-2)
e. -7p2(-2p3+5p)
II. Factoring a monomial from a polynomial
Example 2: find the GCF of the terms 4x3+12x2-8x, then factor the GCF
Exercise 2: find the GCF of the terms of each polynomial then factor
a. 5v2+10v3
b. 3t2-18
c. 4b3-2b2-6b
d. 9x3-6x2+12x
e. x3+7x2-5x
f. 5b3+15b-30
g.
4mn2+8mn
c. 6nm3-12n2m2-24mn
e. 15n3-3n2+12n
f. 6mp6+24p5+18p3
Exercise 4: how do you know if you’ve factored out the GCF of a polynomial? Illustrate your
explanation by using the GCF to factor 10x4+6x3+2x2
13.7 Multiplying Binomials
I. Multiplying Two Binomials
Example 1: using the distributive property
(2x+3) (x+4) =
Example 2:
(2x-3) (x+4) =
Exercise 1 : simplify using Distributive property
a. (6h-7)(2h+3)
b. (9a-8)(7a-4)
c.
II. Multiplying a Trinomial and a Binomial
Example 3: Simplify the product (4x2+x-6)(2x-3)
Exercise 3: Simplify each product
a. (6n-8)(2n2+n+7)
b.
c. 2x(x2+8)(3x2+5)
d. (x-3)(x-4)(x+2)
(9y2+2)(y2-y-1)
(3k2+2)(k+5k2)
Exercise 3:
a. (n2+3)(n+11)
b. (6h-1)(4h2+h+3)
c. (8q-4)(6q2+q+1)
d. (5m+2)(8m-1)
e. (2a+3b)2
f. (y5-9x4)2