Questions: a) (x+9)^2 x^2+2 cdot x cdot 9+9= x^2+18x+81 b) (3-a)^2= 3-a^2 x C) (x+7) cdot(x-7)= x^2-7 x+7 x^2+7 x= x^2-14 x^2 D) (x+2 y) cdot(x-2 y)= x^2-2 y x+2 y x-4 y^2 e) (3 y^2-2)^2=

Transcript text: a) $(x+9)^{2}$ \[ x^{2}+2 \cdot x \cdot 9+9= \\ x^{2}+18 x+81 \] b) \[ (3-a)^{2}= \\ 3-a^{2} x \] C) \[ (x+7) \cdot(x-7)= \\ x^{2}-7 x+7 x^{2}+7 x= \\ x^{2}-14 x^{2} \] D) \[ (x+2 y) \cdot(x-2 y)= \\ x^{2}-2 y x+2 y x-4 y^{2} \] e) $\left(3 y^{2}-2\right)^{2}=$

Solution

Solution Steps

Solution Approach

a) Expand the binomial $(x+9)^2$ using the formula $(a+b)^2 = a^2 + 2ab + b^2$ .

b) Expand the binomial $(3-a)^2$ using the same formula $(a-b)^2 = a^2 - 2ab + b^2$ .

c) Expand the product $(x+7)(x-7)$ using the difference of squares formula $(a+b)(a-b) = a^2 - b^2$ .

Step 1: Expand

(x+9)^2

Using the binomial expansion formula $(a+b)^2 = a^2 + 2ab + b^2$ : $(x+9)^2 = x^2 + 2 \cdot x \cdot 9 + 9^2 = x^2 + 18x + 81$ For $x = 1$ : $(1+9)^2 = 1^2 + 18 \cdot 1 + 81 = 100$

Step 2: Expand

(3-a)^2

Using the binomial expansion formula $(a-b)^2 = a^2 - 2ab + b^2$ : $(3-a)^2 = 3^2 - 2 \cdot 3 \cdot a + a^2 = 9 - 6a + a^2$ For $a = 1$ : $(3-1)^2 = 3^2 - 6 \cdot 1 + 1^2 = 9 - 6 + 1 = 4$

Step 3: Expand

(x+7)(x-7)

Using the difference of squares formula $(a+b)(a-b) = a^2 - b^2$ : $(x+7)(x-7) = x^2 - 7^2 = x^2 - 49$ For $x = 1$ : $(1+7)(1-7) = 1^2 - 49 = 1 - 49 = -48$