What you’ll learn
Recognize structure in expressions.
Key idea
Squaring a whole sum multiplies two equal sums; both cross strips belong to the represented area.
Exponent applies to the complete grouped sum, not only an addend or outer factor; retain both cross strips.
Worked example
Classify examples and non-examples for the concept 'Recognize structure in expressions'.
Read 3(x+7)² without expanding: what happens to the whole grouped quantity before outer multiplication?
- x+7 is one grouped quantity, squared as (x+7)(x+7), then multiplied by 3.
- Each square contains x², two cross strips of area 7x and corner 49; 3 copies yield 3x²+42x+147, including cross coefficient 42.
Answer: The whole sum x+7 is squared — outer factor 3 multiplies the resulting square.
Quick Check
Classify examples and non-examples for the concept 'Recognize structure in expressions'.
Read 6(x+5)² without expanding: what happens to the whole grouped quantity before outer multiplication?