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=+2XY+

(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

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