Simplifying Expressions
Simplifying Expressions
2a(a-5)+4(a-5) The given expression. a*2 Multiply a and 2.
2a^2 2*a*2 = 2a^2.
2a^2*a-5 The distributive property removes the parenthesis.
2a × -5 = -10a Multiply 2a by -5=-10a. -10a
2a^2-10a
+ 4(a-5) Use the distributive property to remove the parentheses.
4*a= 4a 4*-5= -20 Multiply 4 by a-5.
4 × a = 4a 4*-5=-20 Multiply 4 by a, and 4 by -5 4a-20
2a^2-10a + 4a -20 Add the coefficients; combine like terms -10a -10a 10a-10a cancels; subtract negative 10 from 4 to get -6. -10a-4a= -6 2a^2-6a-20 Reorder the terms.
-6a+2a2^2-20 The expression is now simplified. Simplifying Expressions
2w - 3 + 3(w-4) - 5(w – 6) The given expression. The distributive property removes the parentheses.
2w 3w-12 Multiply coefficients and variables: 3*w and 3*-4. 5w-30 Multiply 5*w and 5*-6.
2w + 3w – 12 – 5w -30 Variables are added 2w+3w= 5w. 5w -5w Like terms cancel each other 5w-5w. -3 -12 -30 Bring down -3 from given expression. -3-12= -15 Constants are combined -3-12= -15. -15-(-30) -15-(-30) is 30-15. 30-15 Constants are combined 30-15=15. 15 The expression is now simplified. Simplifying Expressions
0.05(0.3m+35n)-0.8(-0.09n-22m) The given expression.
0.05(0.3m+35n) Distributive property removes the parentheses.
0.05*0.3m & 0.05*35n Distributive property to multiply. 0.015m + 1.75n -0.8(-0.09n-22m) Distributive property removes the parentheses. 0.8*-0.09 & 0.8*-22m Distributive property to multiply. -0.072n - 17.6m
0.015m + 1.75n -0.072n -17.6m Combine like terms: coefficients, variables, constants.
-17.6m -17.6m Like terms cancel out. Combine like terms for m:
2a(a-5)+4(a-5) The given expression. a*2 Multiply a and 2.
2a^2 2*a*2 = 2a^2.
2a^2*a-5 The distributive property removes the parenthesis.
2a × -5 = -10a Multiply 2a by -5=-10a. -10a
2a^2-10a
+ 4(a-5) Use the distributive property to remove the parentheses.
4*a= 4a 4*-5= -20 Multiply 4 by a-5.
4 × a = 4a 4*-5=-20 Multiply 4 by a, and 4 by -5 4a-20
2a^2-10a + 4a -20 Add the coefficients; combine like terms -10a -10a 10a-10a cancels; subtract negative 10 from 4 to get -6. -10a-4a= -6 2a^2-6a-20 Reorder the terms.
-6a+2a2^2-20 The expression is now simplified. Simplifying Expressions
2w - 3 + 3(w-4) - 5(w – 6) The given expression. The distributive property removes the parentheses.
2w 3w-12 Multiply coefficients and variables: 3*w and 3*-4. 5w-30 Multiply 5*w and 5*-6.
2w + 3w – 12 – 5w -30 Variables are added 2w+3w= 5w. 5w -5w Like terms cancel each other 5w-5w. -3 -12 -30 Bring down -3 from given expression. -3-12= -15 Constants are combined -3-12= -15. -15-(-30) -15-(-30) is 30-15. 30-15 Constants are combined 30-15=15. 15 The expression is now simplified. Simplifying Expressions
0.05(0.3m+35n)-0.8(-0.09n-22m) The given expression.
0.05(0.3m+35n) Distributive property removes the parentheses.
0.05*0.3m & 0.05*35n Distributive property to multiply. 0.015m + 1.75n -0.8(-0.09n-22m) Distributive property removes the parentheses. 0.8*-0.09 & 0.8*-22m Distributive property to multiply. -0.072n - 17.6m
0.015m + 1.75n -0.072n -17.6m Combine like terms: coefficients, variables, constants.
-17.6m -17.6m Like terms cancel out. Combine like terms for m: