Monomial x Polynomial
Binomial x Binomial
Binomial x Trinomial
Apply the Pattern
What's the Error?
100

a(4a+3)

4a2+3a

100

(x+8)(x+3)

x2+11x+24

100

(x+5)(x2+4x-8)

x3+9x2+12x-40

100

(x+4)2

= (x)2+2(x)(4)+(4)2

= x2+8x+16

100

(x+5)2

=(x)2 - (5)2

=x2 - 25

Applied the wrong pattern! Should've applied the square of a binomial pattern.

200

2y2(y5-4y)

2y7-8y3

200

(w-7)(w+3)

w2-4w-21

200

(m+3)(m2+4m+7)

m3+7m2+19m+21

200

(a-3)2

= (a)2+2(a)(-3)+(-3)2

= a2-6a+9

200

(x-3)2

= (x)2 + 2(x)(3) + (3)2

= x2 + 6x + 9

The second term is a negative 3 not positive! 

300

3r4(5r2-r+4)

15r6-3r5+12r4

300

(y-1)(y-3)

y2-4y+3

300

(4x-1)(x2-7x+1)

4x3-29x2+11x-1

300

(4m+1)2

= (4m)2+2(4m)(1)+(1)2

= 16m2+8m+1
300

(x-5)(x-2)

= x(x) + x(-2) -5(x) -5(-2)

= x2 -2x -5x +10

= x2 -3x +10

The combined like terms wrong. -2x -5x is -7x. Same sign, add a keep the sign.

400

w3(3w2+2w)+5w4

3w5+7w4

400

(k+4)(3k+2)

3k2+14k+8
400

(2h+3)(2h2+3h+4)

4h3+12h2+17h+12

400

(y-8)(y+8)

= (y)2-(8)2

= y2-64
400

(4m+n)(m-2n)

= 4m(m) +4m(-2n) +n(m) +n(-2n)

= 4m2 -8mn +nm -2n2

-8mn and nm are like terms, even though the n and m are in different spots. These should've been combined to simplify the polynomial to 4m2-7mn-2n2

500

3m(3m+6)-3(m2+4m+1)

6m2+6m-3

500

(2a-4b)(7a-2b)

14a2-32ab+8b2

500

(3x+2)(5x2-12x-2)

15x3-26x2-30x-4

500

(2w+1)(2w-1)

= (2w)2-(1)2

= 4w2-1

500

(t-2)(t+5)

= t -2(t+5)

= t -2(t) -2(5)

= t -2t -10

= -t -10

The distribution was done wrong. t-2 was in parenthesis so the ENTIRE t-2 needed to be multiplied by t+5, not just the -2. You cannot take away or add parenthesis to the original problem. 
M
e
n
u