Expand a product (form-sensitive) <p>Expand and collect like terms: \((x+{@a@})(x+{@b@})\).</p><p>Give your answer as a polynomial in \(x\). [[input:ans]] [[validation:ans]] [[feedback:prt1]]</p> <p>Multiply each term and collect: \(x^2+({@a@}+{@b@})x+{@a@}\cdot{@b@}={@ta@}\).</p><p>A factored expression has the same value, but this task asks for expanded form.</p> 1 0.1 0 2021072200 a:rand(4)+2; b:rand(3)+2; ta:x^2+(a+b)*x+a*b; <p>[[feedback:prt1]]</p> Expansion: (x+a)(x+b) = ta 1 0 0 *10 none 1 i cos-1 lang [ 0 ans algebraic ta 18 1 1 0 1 0 1 1 1 prt1 1.0000000 0 1 0 EqualComAss ans ta 0 = 1.0000000 -1 prt1-0-T <p>Correct: the expression is expanded and collected.</p> = 0.0000000 1 prt1-0-F 1 AlgEquiv ans ta 0 = 0.5000000 -1 prt1-1-T <p>This is equivalent, but expand the product and collect like terms for full credit.</p> = 0.0000000 -1 prt1-1-F <p>Check the middle term and constant term when you multiply the binomials.</p> 17 29 47 1 Expanded polynomial ans ta prt1 1.0000000 0.0000000 prt1-0-T 2 Equivalent but still factored ans (x+a)*(x+b) prt1 0.5000000 0.1000000 prt1-0-F | prt1-1-T 3 Incorrect middle coefficient ans x^2+(a+b+1)*x+a*b prt1 0.0000000 0.1000000 prt1-0-F | prt1-1-F