<p>@pmian</p>
<p>That’s exactly right. You can see that if you have just a little experience recognizing block, these things will start to pop right out at you, and you can answer questions like this in just a few seconds. </p>
<p>@johnstucky</p>
<p>The block method is identical to u-substitution in calculus. The only difference is that on the SAT you will at most have to perform a very simple algebraic manipulation with a block, whereas in Calculus you have to do much more, including “undoing” the block (because usually you want to find x and not u). Note a couple of things:</p>
<p>(1) Blocks appear throughout mathematics. For example, in prealculus you might be asked to solve this equation: x^4-x^2+6=0. Of course you will find them in Calculus, Differential Equations, and more advanced mathematics.</p>
<p>(2) Whatever subject you’re doing, once you get a little practice with blocks, you should begin trying to solve problems without formally doing a substitution. For example, note what pmian did above - he gave the solution without formally changing the problem to x=7u. This will save time. As a simple Calculus example, try integrating xe^(x^2) quickly in your head without formally substituting.</p>
<p>(3) As far as I know, I am the only one that uses the word “block” to describe these substitutions. But especially on the SAT I think this word helps to emphasize my point.</p>