Distribute and Calculate: Distribute the -3 inside the parentheses to both terms 2j and -5k^2. Calculation: -3 * 2j = -6j and -3 * -5k^2 = 15k^2 So, the expression inside the parentheses becomes -6j + 15k^2.Square Expression: Square the entire expression inside the parentheses. Calculation: (-6j + 15k^2)^2 This means we need to multiply the expression by itself: (-6j + 15k^2) * (-6j + 15k^2)Apply FOIL Method: Apply the distributive property (FOIL method) to multiply the two binomials. Calculation: (-6j)^2 + 2(-6j)(15k^2) + (15k^2)^2Calculate Terms: Calculate each term separately. Calculation: (-6j)^2 = 36j^2, 2(-6j)(15k^2) = -180jk^2, and (15k^2)^2 = 225k^4 So, the expanded form is 36j^2 - 180jk^2 + 225k^4Combine for Final Result: Combine the calculated terms to get the final result. Calculation: 36j^2 - 180jk^2 + 225k^4

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$[-3(2j-5k^2)]^2$

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Math Problems

Grade 8

Understanding negative exponents

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[-3(2j-5k^2)]^2

Distribute and Calculate: Distribute the $-3$ inside the parentheses to both terms $2j$ and $-5k^2$ . $\newline$ Calculation: $-3 \times 2j = -6j$ and $-3 \times -5k^2 = 15k^2$ $\newline$ So, the expression inside the parentheses becomes $-6j + 15k^2$ .
Square Expression: Square the entire expression inside the parentheses. $\newline$ Calculation: $(-6j + 15k^2)^2$ $\newline$ This means we need to multiply the expression by itself: $(-6j + 15k^2) \times (-6j + 15k^2)$
Apply FOIL Method: Apply the distributive property (FOIL method) to multiply the two binomials. $\newline$ Calculation: $(-6j)^2 + 2(-6j)(15k^2) + (15k^2)^2$
Calculate Terms: Calculate each term separately. $\newline$ Calculation: $(-6j)^2 = 36j^2$ , $2(-6j)(15k^2) = -180jk^2$ , and $(15k^2)^2 = 225k^4$ $\newline$ So, the expanded form is $36j^2 - 180jk^2 + 225k^4$
Combine for Final Result: Combine the calculated terms to get the final result. $\newline$ Calculation: $36j^2 - 180jk^2 + 225k^4$