Identify Expression: Identify the expression to be expanded. The expression to be expanded is (x+3)^2, which is a binomial squared.Apply Binomial Square Formula: Apply the binomial square formula. The binomial square formula is (a+b)^2 = a^2 + 2ab + b^2. Here, a = x and b = 3. So, (x+3)^2 = x^2 + 2*x*3 + 3^2.Perform Multiplication: Perform the multiplication. Now we calculate each term: x^2, 2*x*3 = 6x, and 3^2 = 9. So, (x+3)^2 = x^2 + 6x + 9.Multiply by 4: Multiply the expanded binomial by 4. We have 4(x^2 + 6x + 9), which means we need to distribute the 4 to each term inside the parentheses. 4*x^2 = 4x^2, 4*6x = 24x, and 4*9 = 36. So, 4(x+3)^2 = 4x^2 + 24x + 36.Subtract 8: Subtract 8 from the result of step 4. Now we have 4x^2 + 24x + 36 - 8. Subtracting 8 from 36 gives us 28. So, y = 4x^2 + 24x + 28.

Grade 8

Understanding negative exponents

Full solution

y=4(x+3)^2-8

Identify Expression: Identify the expression to be expanded. $\newline$ The expression to be expanded is $(x+3)^2$ , which is a binomial squared.
Apply Binomial Square Formula: Apply the binomial square formula. $\newline$ The binomial square formula is $(a+b)^2 = a^2 + 2ab + b^2$ . Here, $a = x$ and $b = 3$ . $\newline$ So, $(x+3)^2 = x^2 + 2\times x\times 3 + 3^2$ .
Perform Multiplication: Perform the multiplication. $\newline$ Now we calculate each term: $x^2$ , $2 \times x \times 3 = 6x$ , and $3^2 = 9$ . $\newline$ So, $(x+3)^2 = x^2 + 6x + 9$ .
Multiply by $4$ : Multiply the expanded binomial by $4$ . $\newline$ We have $4(x^2 + 6x + 9)$ , which means we need to distribute the $4$ to each term inside the parentheses. $\newline$ $4\times x^2 = 4x^2$ , $4\times 6x = 24x$ , and $4\times 9 = 36$ . $\newline$ So, $4(x+3)^2 = 4x^2 + 24x + 36$ .
Subtract $8$ : Subtract $8$ from the result of step $4$ . $\newline$ Now we have $4x^2 + 24x + 36 - 8$ . $\newline$ Subtracting $8$ from $36$ gives us $28$ . $\newline$ So, $y = 4x^2 + 24x + 28$ .