Algebraic Expression The algebraic expressions have the variables and the constants. The algebraic expressions are the finite combination of the symbols that are formed according to the rules of the context. The algebra is an expression which is used to designate the value for the given values in the expression. The expression might be depending on the values assigned to the values assigned in the expression. The expression is the syntactic concept in the algebra. The online provides the connectivity between the tutors and the students. This article has the information about learn online algebraic expressions. Simplifying Algebraic Expressions Below are the examples on Simplifying algebraic expressions Know More About Adding and Subtracting Fractions Worksheets
Example 1 Compute the factors for the expression x2+ 56x+ 768. Solution: The given expression is x2+ 56x+ 768. Step 1: x2+ 56x+ 768 = x2+24x+ 32x+ (24x 32) Step 2: x2+ 56x+ 768 = x(x+24) + 32(x +24) Step 3: x2+ 56x+ 768 = (x+24) (x+32) Step 4: x+24 and x+32 The factors for the given expression x2+ 56x+ 768 are (x +24) and (x +32). Example 2 Compute the factors for the expression x2+ 76x+ 1440. Solution :- The given expression is x2+ 76x+ 1440. Step 1: x2+ 76x+ 1440 = x2+36x+ 40x+ (36x 40) Step 2: x2+ 76x+ 1440 = x(x+36) + 40(x +36) Learn More About Decimal Worksheets
Step 3: x2+ 76x+ 1440 = (x+36) (x+40) Step 4: x+36 and x+40 The factors for the given expression x2+ 76x+ 1440 are (x +36) and (x +40). Example 3 Simplify the expression 24xy + 10 x2y + 14 x y + 16 x2y + 10 x y. Solution :The given expression is 24xy + 10 x2y + 14 x y + 16 x2y + 10 x y. Step 1: 24xy + 10 x2y + 14 x y + 16 x2y + 10 x y = x y (24 +14 +10) + x2y (10+ 16) Step 2: 24xy + 10 x2y + 14 x y + 16 x2y + 10 x y = 48 x y + x2y (10+ 16) Step 3: 24xy + 10 x2y + 14 x y + 16 x2y + 10 x y = 48 x y + 26 x2y The value for the given expression 12xy + 13 x2y + 16 x y + 20 x2y is 48 x y + 26 x2y. Algebraic Expressions Practice Problems Below are the practice problems on algebraic expressionsDetermine the value for the algebraic expression x2+ 50x+ 600. Answer: (x + 30) (x + 20) Simplify the expression 80 x y + 15 x2y + 5 x y + 17 x2y. Answer: 85 x y + 32 x2y.
Perfect Square Trinomial Introduction: Perfect Square Trinomial is the product of two binomials but both the binomials are same. When factoring some quadratics which gives identical factors, that quadratics are Perfect Square Trinomial. The general form of perfect square trinomial is (ax-b) 2 =(ax)2-2axb+b2 and (ax+b) 2=(ax)2+ 2axb + b2. In this, the first term and last term of the perfect square are perfect squares and the middle term is 2 times the Square root of first terms times and square root of last terms. Perfect Square Trinomial Example Problems x2+4x+4 =0 In this the first term is x2, the second term is 2 times the square root of first term and square root of second term and the third term 4 can be written as 22 which is a perfect square. x2+2 Ă— Ă— + 22 = 0. This is the perfect square trinomial.
x2+8x+16=0 In this the first term is x2, the second term is 2 times the square root of first term and square root of second term and the third term 16 can be written as 42 which is a perfect square. x2+ 2 × × + 42 = 0. This is the perfect square trinomial. x2+10x+5 × 5 = 0 In this the first term is x2, the second term is 2 times the square root of first term and square root of second term and the third term 25 can be written as 52 which is a perfect square. x2+2 × × + 52 = 0. This is the perfect square trinomial. Factoring Perfect Square TrinomialBack to Top Factor the trinomial x2+4x+4=0 Solution: Given, x2+4x+4=0 The above trinomial can be written as, x2+2x+2x+4=0 Read More About Graphing Worksheets
Take x as common from first two terms, x(x+2)+2x+4=0 Take 2 as common from last two terms. x(x+2)+2(x+2)=0 (x+2)(x+2)=0 In this it is the product of two identical binomials (x+2)2=0, which is a perfect square.
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