Q&A for How to Simplify Math Expressions

There really is no difference to the final result based on which mnemonic method you use. PEMDAS is really the same thing. P stands for "parentheses," which is BODMAS refers to as brackets. The M and D are together and are to be evaluated left to right. The A and S are together and are to be evaluated left to right.

-3(2a² - 5) + 3a(4a - 5) = (-6a² + 15) + (12a² - 15a) = (-6a² + 12a²) + (15 ) + (-15a) = 6a² -15a + 15 = 3(2a² -5a + 5).

To simplify a math expression without parentheses, you follow the order of operations, which is PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction). Because the expression has no parentheses, you can start checking the expression for exponents. If it does, simplify that first. Then, you can move on to multiplication and division, then finally, addition and subtraction.

The coefficients are 24 and 4 (or you can call them +24 and +4).

First, write all those fractions with a common denominator: 30/60, 40/60, 45/60, and 48/60. The highest common (integer) factor of those fractions is the hcf of their numerators over that common denominator. The hcf of 30, 40, 45, and 48 is 1 (as it always is when you use the least common denominator), so the hcf of 1/2, 2/3, 3/4, and 4/5 is 1/60.

Replace each letter in the expression with its given value: (-2) + [-(3)] + (½)(-2) = (-2) - (3) +(-1) = -2 -3 -1 = -6.

Just like 2+2+2+2 is the same as 2x4 a+a+a+a is the same as ax4 or 4a. Remember that multiplication is merely repeated addition.

The typical graph of a cubic function looks similar to an "S" curve, centered on the origin, with one half being an inverted mirror image of the other.

To eliminate the denominators, multiply both sides of the equation by 12 (which is 4x3): (3x) + (4x) = 12. Combine like terms: 7x = 12. Divide both sides by 7: x = 12/7 = 1 5/7.

Dividing by a number that has a negative exponent is the same as multiplying by that same number except with a positive exponent. For example, 2 / (3^-2) = (2)(3^2) = 18.

18m / 9 simplifies to 2m, but you can't "solve" this expression without an equation.

Think of this as multiplying four terms together: 2, 3, and two x terms each with their own exponent. 2 multiplied by 3 equals 6. x^5y multiplied by x^2y equals x^7y (you just add the exponents together). So the final product is 6x^7y.

This expression starts with a negative number and then adds another negative number. You can visualize this by using a "number line": -42 is 42 units to the left of zero on the negative side of the number line. Adding a negative number means moving further to the left. 17 units to the left of -42 is -59.

8 - 3 = 5.

(0.004)(30,000)² = (4 x 10^-3)(3 x 10^4)(3 x 10^4) = 4 x 3 x 3 x 10^5 = 36 x 10^5 = 3.6 x 10^6 = 3,600,000.

10 2/3 + 3 1/6 + 7 2/9 = 10 12/18 + 3 3/18 + 7 4/18 = 20 19/18 = 21 1/18.

The general rule is: a/b/c = a(c/b). So 10 / 6 / 15 = 10(15/6) = 150 / 6 = 25.

a [5x + 4] = 5ax + 4a.

A = (r + t)² - r² = (r² + 2rt + t²) - r² = 2rt + t² = A. Then 2rt = A - t², and r = (A - t²) / 2t.

2 2/3 + 3 3/4 + 4 4/5 = 2 40/60 + 3 45/60 + 4 48/60 = 9 133/60 = 11 13/60.

1/3 + 4/6 = 2/6 + 4/6 = 6/6 = 1.

a²x² - b²y² / axby cannot be simplified. The terms in the denominator do not cancel any of the terms in the numerator because of the minus sign.

Take the cube root of both sides. You have to ask yourself: What, multiplied by itself twice, will give you 125. The answer is +/- 5. So x = +/- 5 (plus or minus 5).

Combine like terms: 2a - 2ab = 2a(1 - b).

Do what is inside the parentheses first: (48) ÷ 6 x 9 - 2 + 6 x (6). Now do the multiplication and division from left to right: (48 ÷ 6 x 9) - 2 + (6 x 6) = (8 x 9) - 2 + (36) = 72 - 2 + 36 = 110.

[(x² - 9) / (4x - 12)] ÷ [(x + 3) / 3] = [(x² - 9) / (4x - 12)][3 / (x + 3)] = [(x - 3)(x + 3)] / [4(x - 3)][3 / (x + 3)] = [(x + 3) / 4][3 / (x + 3)] = 3/4. The original expression simplifies to 3/4.

√2 equals 1.41421356.... It is a decimal number with a very large number of non-repeating digits. Therefore, it cannot be exactly expressed as a fraction (the ratio of two integers). That makes it an irrational number.

(27 1/3)² = (82/3)² = 82² / 3² = 6724 / 9 = 747.11.

7 - 3 3/8 - 2 1/4 = 7 - 27/8 - 9/4 = 56/8 - 27/8 - 18/8 = 11/8 = 1 3/8.

y(2y - 4) + y(y + 6) = y(2y - 4 + y + 6) = y(3y + 2).