1.
A. 56x8y5
2.
-4z(8z3 – 3z2 + 7)
= (-4z)(8z3) + (-4z)(-3z2) + (-4z)(7)
= -32z4 + 12z3 – 28z
3.
A. x2 - 1
4.
(x + 8)2
= (x + 8)(x + 8)
= x(x) + 8(x) + 8(x) + 8(8)
= x2 + 8x + 8x + 64
= x2 + 16x + 64
5.
(y – 9)2
= (y – 9)(y – 9)
= y(y) – 9(y) – 9(y) – 9(-9)
= y2 – 9y – 9y + 81
= y2 – 18y + 81
6.
(y2 – 5y – 2)(y + 8)
= y2(y) + y2(8) – 5y(y) – 5y(8) – 2(y) – 2(8)
= y3 + 8y2 – 5y2 – 40y – 2y – 16
= y3 + 3y2 – 42y – 16
7.
Area of top = (2x – 7y cm)(2x + 7y cm)
= 2x(2x) – 7y(2x) + 2x(7y) – (7y)(7y) cm2
= 4x2 – 14xy + 14xy – 49y2 cm2
= 4x2 – 49y2 cm2
8.
Area of garden = (9x – 8y ft)(5x – 3y ft)
= 9x(5x) + 9x(-3y) – 8y(5x) – 8y(-3y) ft2
= 45x2 – 27xy – 40xy + 24y2 ft2
= 45x2 – 67xy + 24y2 ft2
9.
x 2 " 25 ( x + 5)( x " 5)
=
= x "5
x +5
( x + 5)
10.
25x 2 "100y 2 (5x "10y )(5x +10y )
=
= 5x "10y
5x +10y
(5x +10y )
!
! 11.
(x – 0.1)(x + 0.1)
= x(x) + x(0.1) – x(0.1) – 0.1(0.1)
= x2 + 0.1x – 0.1x – 0.01
= x2 – 0.01
12.
Term
3p
-pq
-7p2q3
-8pq6
Coefficient
3
-1
-7
-8
The degree of the polynomial is 7
13.
t 2 " 2t + 3
t +1 t 3 " t 2 + t "1
)
t3 + t2
0 " 2t 2 + t
" 2t 2 " 2t
0 + 3t "1
3t + 3
0"4
Solution : t 2 " 2t + 3 "
!
!
4
t +1
Degree
1
2
5
7
#
4 &
Check : % t 2 " 2t + 3 "
(( t +1)
$
t +1'
# 4 &
= ( t 2 " 2t + 3)( t +1) " %
(( t +1)
$ t +1'
= ( t 2 " 2t + 3)( t +1) " 4
= t 2 ( t ) + t 2 (1) " 2t ( t ) " 2t (1) + 3( t ) + 3(1) " 4
= t 3 + t 2 " 2t 2 " 2t + 3t + 3 " 4
= t 3 " t 2 + t "1
Checks.
!