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

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

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Identify expression and exponents: Identify the expression inside the brackets and the exponents. The expression inside the brackets is (2j-5k)^2, and it is being squared again by the outer exponent of 2.Square expression inside brackets: Square the expression inside the brackets. To square (2j-5k)^2, we multiply the expression by itself: (2j-5k)*(2j-5k).Use FOIL method to expand: Use the FOIL method (First, Outer, Inner, Last) to expand the expression. (2j-5k)*(2j-5k) = (2j*2j) + (2j*-5k) + (-5k*2j) + (-5k*-5k)Simplify terms from expansion: Simplify the terms from the FOIL expansion. (2j*2j) = 4j^2, (2j*-5k) = -10jk, (-5k*2j) = -10jk, (-5k*-5k) = 25k^2 So, (2j-5k)^2 = 4j^2 - 10jk - 10jk + 25k^2Combine like terms: Combine like terms from the simplified FOIL expansion. -10jk - 10jk = -20jk So, (2j-5k)^2 = 4j^2 - 20jk + 25k^2Apply outer exponent: Apply the outer exponent of 2 to the squared expression. [-3(4j^2 - 20jk + 25k^2)]^2 means we need to square -3 and multiply it by the square of the expression (4j^2 - 20jk + 25k^2).Square coefficient -3: Square the coefficient -3. (-3)^2 = 9Square trinomial expression: Square the expression (4j^2 - 20jk + 25k^2). When squaring a trinomial, each term is squared and the cross-products are doubled. (4j^2)^2 = 16j^4, (-20jk)^2 = 400j^2k^2, (25k^2)^2 = 625k^4Calculate cross-products: Calculate the cross-products and double them. The cross-products are 2*(4j^2*-20jk) and 2*(-20jk*25k^2). 2*(4j^2*-20jk) = -160j^3k, 2*(-20jk*25k^2) = -1000jk^3Combine squared terms: Combine the squared terms and the doubled cross-products. 16j^4 + (-160j^3k) + 400j^2k^2 + (-1000jk^3) + 625k^4Multiply by squared coefficient: Multiply the combined expression by the squared coefficient 9. 9*(16j^4 - 160j^3k + 400j^2k^2 - 1000jk^3 + 625k^4)Distribute coefficient to terms: Distribute the coefficient 9 to each term in the expression. 9*16j^4 = 144j^4, 9*-160j^3k = -1440j^3k, 9*400j^2k^2 = 3600j^2k^2, 9*-1000jk^3 = -9000jk^3, 9*625k^4 = 5625k^4Combine distributed terms: Combine the distributed terms to get the final expression. 144j^4 - 1440j^3k + 3600j^2k^2 - 9000jk^3 + 5625k^4

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

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

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