Q&A for How to Simplify Algebraic Expressions

To simplify algebraic expressions, the acronym PEMDAS is commonly used. It stands for Parentheses, Exponents, Multiplication, Division, Addition. and Subtraction. You do these operations in the order they appear. So first, you do what is in the parenthesis. Then, you calculate the exponents. Then you do multiplication and division, then finally, you add and subtract.

Simplify by multiplying like terms together: (-3)(4) = -12. (a^2)(a^5) = a^7. (b^2)(b^3) = b^5. The final product is -12a^7b^5.

(p² - 9) is the difference of squares and factors to (p + 3)(p - 3). (2p + 6) factors to 2(p + 3). (p² - 9) / (2p + 6) = (p + 3)(p - 3) / 2(p + 3) = (p - 3) / 2.

First perform the indicated multiplications. Then combine terms.

Perform the multiplication a second time (even a third time), and see if you get the same product.

You can't do much with it. All you can do is: 5(b-c) + 19a + 6d.

In algebra letters are used to indicate unknown quantities.

Factor a 2 out of the factor in parentheses: 6x(x² - 2x + 1). Then factor what remains in the parentheses: 6x (x - 1)(x - 1) = 6x (x - 1)².

First do the multiplication: (6a +30) + 7 = 11a - 12. Then do the adding: 6a + 37 = 11a - 12. Now subtract 6a from both sides, and add 12 to both sides: 49 = 5a. Divide by 5: 9.8 = a. (An unusual result, but there it is.)

First remove the parentheses. Then combine like terms. Then factor out any common factors: 5x² + 2x - (3x² - 2) = 5x² + 2x - 3x² + 2 = 2x² + 2x + 2 = 2(x² + x + 1).

Let's borrow the example from Method 1 Step 3 above, because it's simple and straightforward: (3 + 2)² - 40/2 + 3 x 2. "P" means do whatever is inside parentheses first: 3 + 2 = 5. So now we have 5² - 40/2 + 3 x 2. "E" means we apply exponents: 5² = 25. So now we have 25 - 40/2 + 3 x 2. "MD" means we multiply and divide from left to right: 40/2 = 20, and 3 x 2 = 6. So now we have 25 - 20 + 6. Finally, "AS" means we add and subtract from left to right: 25 - 20 = 5, and 5 + 6 = 11, the final answer.

Before we can subtract, we have to make the two denominators the same. So multiply the first term by 8y/8y, and the second term by 6y/6y. (In each case we are multiplying by 1 and thus not changing any values -- only the forms they take.) The result of the multiplication: (40xy / 48y²) - (42xy / 48y²). Now perform the subtraction: -2xy / 48y². That simplifies to -x / 24y. All we accomplished here is turning two terms into one term, which qualifies as a simplification.

PEMDAS is the mnemonic for the order of operations. If you don't, you may do stuff incorrectly and end up with false results, which aren't correct.

In division, when the base of the numerator is the same as the base of the denominator, just subtract the denominator's exponent from the numerator's exponent. So y^8 / y^-5 = y^[8 - (-5)] = y^13.

(15x + 5) / (3x + 1) = 5(3x + 1) / (3x + 1) = 5.

Let's assume the expression is (4x - 4y) / (2y - 2x). In the numerator, factor out a 4. In the denominator, factor out a (-2). That makes the expression 4(x - y) / -2(x - y). After canceling, we're left with 2/-1, which simplifies to -2.

(4x - 4y) / (2y - 2x) = 2(2x - 2y) / (-2x + 2y) = 2(2x - 2y) / [(-1)(2x - 2y)] = 2 / -1 = -2.

6 + a + a = 6 + 2a = 10. Subtract 6 from both sides: 2a = 4. Divide both sides by 2: a = 2.

(8-10)(5+10) = (-2)(15) = -30.

Your expression would equal to 8a-8, since 16/2 = 8. 8(a-1) would be your answer.

Yes. First, take away the parenthesis. 2x-4 - 6x - 6 = -4x - 10. This would be the answer.

Find the cube root of both sides of the equation: the cube root of n³ is n. The cube root of 8 is 2. So n = 2.

(x - 5)(x + 6) = x² + 6x - 5x - 30 = x² + x - 30.

It's called factoring, Think of factoring an expression with exponents as dividing that expression by one of its factors. A factor of an expression is a number or expression that divides into the expression evenly.

12x - 6 + 4x² = 4x² +12x - 6 = 2(2x² + 6x - 3).

As you have written it, the expression is as simplified as it can get.

Combine like terms: (7n - 8n) + (k - 8k) + 3m = (-n) + (-7k) + 3m = -n -7k + 3m = 3m - n - 7k.

If you mean [20(x^6)] / 5x, you divide 20 by 5, and x^6 by x to get 4(x^5).