Let's simplify each expression step-by-step:
a) 520
Simplify 20:
20=4×5=25
So, the expression becomes:
5×25=105
b) 28+37
Simplify 28:
28=4×7=27
So, the expression becomes:
27+37=57
c) 38−218
Simplify 8 and 18:
8=4×2=22and18=9×2=32
So, the expression becomes:
3×22−2×32=62−62=0
d) 27×32
Multiply the terms:
(2×3)×(7×2)=614
e) 25×20
Simplify 20:
20=25
Multiply the terms:
25×25=4×5=20
f) 1512÷53
Simplify 12:
12=4×3=23
Divide the terms:
5315×23=53303=6
g) 3(3+15)
Distribute 3:
3×3+3×15=3+45
Simplify 45:
45=9×5=35
So, the expression becomes:
3+35
h) (7+2)2
Expand using the square of a binomial:
(7+2)2=(7)2+2(7)(2)+(2)2=7+214+2=9+214
i) (5+6)(2+5)
Expand using FOIL (First, Outside, Inside, Last):
5×2+5×5+6×2+6×5=10+5+12+30
Simplify 12:
12=23
So, the expression becomes:
10+5+23+30
Would you like more details on any specific problem, or do you have any questions?
Related Questions:
- How do you simplify expressions with multiple radicals?
- What are the rules for multiplying and dividing square roots?
- How can you simplify expressions with binomials involving radicals?
- What are common mistakes when working with radicals?
- How do you expand and simplify expressions using the distributive property?
Tip: Always simplify the radicals first before performing other operations; this often makes the calculations easier!