Square of sum: System of equations with no solution

Equations with Variables on One SideUsing short multiplication formulasUsing variablesEquations with denominatorsComplete the missing numbersIdentify the greater valueUsing fractionsUsing quadrilateralsMore than one factorizationData with powers and rootsUsing multiple rulesNumber of termsEquations with variables on both sidesSolving the problemTransition between expressionsResulting in a quadratic equation
Question 1

Choose the expression that has the same value as the following:


(x+3)2 (x+3)^2

Question 2

(2[x+3])2= (2\lbrack x+3\rbrack)^2=

Question 3

2(x+3)2+3(x+2)2= 2(x+3)^2+3(x+2)^2=

Question 4

(x2+4)2= (x^2+4)^2=

Question 5

(x+x2)2= (x+x^2)^2=

Examples with solutions for Square of sum: System of equations with no solution

Exercise #1

Choose the expression that has the same value as the following:


(x+3)2 (x+3)^2

Video Solution

Step-by-Step Solution

We use the abbreviated multiplication formula:

x2+2×x×3+32= x^2+2\times x\times3+3^2=

x2+6x+9 x^2+6x+9

Answer

x2+6x+9 x^2+6x+9

Exercise #2

(2[x+3])2= (2\lbrack x+3\rbrack)^2=

Video Solution

Step-by-Step Solution

We will first solve the exercise by opening the inner brackets:

(2[x+3])²

(2x+6)²

We will then use the shortcut multiplication formula:

(X+Y)²=X²+2XY+Y²

(2x+6)² = 2x² + 2x*6*2 + 6² = 2x+24x+36

Answer

4x2+24x+36 4x^2+24x+36

Exercise #3

2(x+3)2+3(x+2)2= 2(x+3)^2+3(x+2)^2=

Video Solution

Step-by-Step Solution

In order to solve the exercise, remember the abbreviated multiplication formulas:

(x+y)2=x2+2xy+y2 (x+y)^2=x^2+2xy+y^2

Let's start by using the property in both cases:

(x+3)2=x2+6x+9 (x+3)^2=x^2+6x+9

(x+2)2=x2+4x+4 (x+2)^2=x^2+4x+4

We then reinsert them back into the formula as follows:

2(x2+6x+9)+3(x2+4x+4)= 2(x^2+6x+9)+3(x^2+4x+4)=

2x2+12x+18+3x2+12x+12= 2x^2+12x+18+3x^2+12x+12=

5x2+24x+30 5x^2+24x+30

Answer

5x2+24x+30 5x^2+24x+30

Exercise #4

(x2+4)2= (x^2+4)^2=

Video Solution

Answer

x4+8x2+16 x^4+8x^2+16

Exercise #5

(x+x2)2= (x+x^2)^2=

Video Solution

Answer

x2+2x3+x4 x^2+2x^3+x^4

Question 1

Simplify the expression (x+y+1)2 (x+y+1)^2

Question 2

y=x2+9x+24 y=x^2+9x+24

Which expression should be added to y so that:

y=(x+5)2 y=(x+5)^2

Exercise #6

Simplify the expression (x+y+1)2 (x+y+1)^2

Video Solution

Answer

x2+2x+y2+2y+2xy+1 x^2+2x+y^2+2y+2xy+1

Exercise #7

y=x2+9x+24 y=x^2+9x+24

Which expression should be added to y so that:

y=(x+5)2 y=(x+5)^2

Video Solution

Answer

x+1 x+1