Square of sum: System of equations with no solution

Question 1

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

$$ (x+3)^2 $$

Question 2

$(2\lbrack x+3\rbrack)^2=$

Question 3

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

Question 4

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

Question 5

$$ (x+x^2)^2= $$

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:

$(x+3)^2$

Video Solution

Step-by-Step Solution

We use the abbreviated multiplication formula:

$x^2+2\times x\times3+3^2=$

$x^2+6x+9$

Answer

$x^2+6x+9$

Exercise #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

$4x^2+24x+36$

Exercise #3

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

Video Solution

Step-by-Step Solution

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

$(x+y)^2=x^2+2xy+y^2$

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

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

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

We then reinsert them back into the formula as follows:

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

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

$5x^2+24x+30$

Answer

$5x^2+24x+30$

Exercise #4

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

Video Solution

Answer

$x^4+8x^2+16$

Exercise #5

$(x+x^2)^2=$

Video Solution

Answer

$x^2+2x^3+x^4$

Question 1

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

Question 2

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

Which expression should be added to y so that:

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

Exercise #6

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

Video Solution

Answer

$x^2+2x+y^2+2y+2xy+1$

Exercise #7

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

Which expression should be added to y so that:

$y=(x+5)^2$

Video Solution

Answer

$x+1$